The complete reference table of the first 100 perfect cubes — plus a calculator that cubes any integer, checks whether a number is a perfect cube, and finds the nearest perfect cubes above and below it.
A perfect cube is an integer you get by multiplying another integer by itself three times. The first few are impossible to forget once you see them: 1, 8, 27, 64, 125 — the cubes of 1, 2, 3, 4, and 5. They grow fast. By the time you reach the 100th perfect cube, you are looking at 1,000,000, the cube of 100. This page gives you the complete reference table of the first 100 perfect cubes, a calculator that cubes any integer instantly, a checker that tells you whether any number is a perfect cube, and the nearest perfect cubes above and below any value you enter.
Perfect cubes show up constantly in school mathematics and in real measurement. Any time you compute the volume of a cube-shaped box, tank, or room, you are cubing a length. Any time you take a cube root — of a volume to recover an edge length, of a number in an algebra problem — you are asking “which perfect cube is this near, or exactly?” Memorizing the first dozen perfect cubes, and knowing how to look up the rest, turns cube-root estimation from guesswork into a two-second mental task. Engineers use perfect cubes when sizing cubic containers; carpenters meet them when a cubic foot of material is the ordering unit; students meet them in every chapter on exponents and radicals.
The table below lists the first 20 perfect cubes for quick reference. Use the calculator above, or the “Show the First 100 Perfect Cubes Table” button inside it, to see all 100.
| n | n³ | n | n³ |
|---|---|---|---|
| 1 | 1 | 11 | 1,331 |
| 2 | 8 | 12 | 1,728 |
| 3 | 27 | 13 | 2,197 |
| 4 | 64 | 14 | 2,744 |
| 5 | 125 | 15 | 3,375 |
| 6 | 216 | 16 | 4,096 |
| 7 | 343 | 17 | 4,913 |
| 8 | 512 | 18 | 5,832 |
| 9 | 729 | 19 | 6,859 |
| 10 | 1,000 | 20 | 8,000 |
The widget at the top of this page does three jobs at once. First, it cubes any integer you type: enter 12 and it returns 1,728. Second, it tells you whether your number is itself a perfect cube — enter 1,728 and it confirms that 1,728 = 12³. Third, when your number is not a perfect cube, it reports the nearest perfect cubes below and above it, each with its cube root, which is exactly the bracketing information you need to estimate a cube root by hand.
To use it, type any integer from −1,000,000 to 1,000,000 into the input box and press “Cube It and Check.” The result panel shows the cube, the yes/no perfect-cube verdict, the bracketing cubes when relevant, and the decimal cube root as a cross-check. Press “Reset” to restore the default value of 12. To browse the entire reference, press “Show the First 100 Perfect Cubes Table” — a scrollable table of n and n³ for n = 1 through 100 appears inside the widget, and pressing the button again hides it.
A handy workflow for estimation: suppose you need ∛(500) without a calculator. Enter 500. The widget tells you it is not a perfect cube, that the nearest cube below is 343 = 7³, and the nearest above is 729 = 8³. You now know ∛(500) is between 7 and 8, closer to 8 — the true value is about 7.94. That bracketing technique is the classic pencil-and-paper cube-root method, and this widget automates the lookup step.
A perfect cube is the cube of an integer: a number of the form n³ where n is a whole number (positive, negative, or zero). The name comes from geometry — n³ is the volume of a cube whose edge length is n — just as a perfect square n² is the area of a square with side n. The sequence begins 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1,000, and continues forever, growing roughly like the cube of the index.
Every positive integer sits somewhere in the landscape defined by perfect cubes. The cube root ∛x asks “which number, cubed, gives x?” When x is a perfect cube, the answer is a clean integer: ∛(1,728) = 12. When x is not, the answer is an irrational decimal trapped between two consecutive integers, and the perfect cubes on either side are its fences. This is why the table is a reference tool rather than a curiosity: it converts cube-root questions into table lookups.
Perfect cubes grow much faster than perfect squares. The gap between consecutive cubes near n is about 3n², so while the squares 100 and 121 differ by 21, the cubes 1,000 and 1,331 differ by 331. That widening gap is why cube-root estimation gets easier, in a relative sense, for large numbers — but also why memorizing cubes past 12 or so gives way to reference tables and calculators. Negative integers have perfect cubes too: (−5)³ = −125, because three negatives multiply to a negative. Zero is a perfect cube as well, since 0³ = 0.
There is a beautiful digit pattern worth knowing: the last digit of a perfect cube determines the last digit of its root uniquely. Cubes ending in 0, 1, 4, 5, 6, 9 come from roots ending in the same digit; a cube ending in 8 comes from a root ending in 2; ending in 7 from a root ending in 3; ending in 3 from a root ending in 7; ending in 2 from a root ending in 8. Mental-math enthusiasts use this to extract cube roots of perfect cubes like 140,608 (∛ = 52) in seconds: the last digit 8 means the root ends in 2, and 140,608 sits between 125,000 (50³) and 216,000 (60³), so the root is 52.
n³ = n × n × n
x is a perfect cube ⟺ ∛x is an integer
The definition is a single multiplication done three times: 9³ = 9 × 9 × 9 = 729. The test for perfect-cube-ness runs the other direction: take the cube root, and check whether it is an integer. In symbols, x is a perfect cube exactly when ∛x ∈ ℤ. The calculator applies this test with a rounding step — it rounds ∛x to the nearest integer r and checks whether r³ equals x exactly — which avoids the tiny floating-point dust that direct equality tests would trip over.
Two companion identities are useful. The difference of consecutive cubes factors as (n+1)³ − n³ = 3n² + 3n + 1, which explains the widening gaps. And the sum of the first n cubes has a closed form: 1³ + 2³ + ⋯ + n³ = (n(n+1)/2)² — the square of the triangular number, a result sometimes called Nicomachus’s theorem. For n = 10, the cubes sum to (55)² = 3,025.
Example 1 — Cubing 15. 15³ = 15 × 15 × 15. First 15 × 15 = 225, then 225 × 15 = 3,375. So 15³ = 3,375, which matches row 15 of the table. Entering 15 in the widget returns 3,375 and confirms 3,375 is a perfect cube (it is 15³).
Example 2 — Is 2,000 a perfect cube? The table shows 12³ = 1,728 and 13³ = 2,197, and 2,000 falls between them, so it cannot be a perfect cube. The widget agrees: not a perfect cube, nearest below 1,728 = 12³, nearest above 2,197 = 13³, and ∛(2,000) ≈ 12.599. This bracketing immediately tells you the cube root to one decimal place of context.
Example 3 — Cubing a negative: (−9)³. (−9) × (−9) = 81, then 81 × (−9) = −729. So (−9)³ = −729, a negative perfect cube. The widget handles negatives the same way: enter −9, get −729, and the verdict “yes, −729 = (−9)³.”
Example 4 — A volume problem. A cubic storage tank holds 4,096 liters, and 1 liter = 1 cubic decimeter, so the tank’s volume is 4,096 dm³. What is its edge length? Scan the table: 16³ = 4,096. The edge is 16 dm (1.6 m). No algebra required — the table turns a cube-root problem into a lookup.
Shipping and packaging. Parcel volumes scale with the cube of the linear dimension, so doubling a box’s side multiplies its volume by 8 = 2³. Logistics planners use this constantly: a 30 cm cube holds 27,000 cm³ (27 liters), while a 40 cm cube holds 64,000 cm³ (64 liters) — not “a third more” but nearly two and a half times as much. The perfect-cube table makes these comparisons instant.
Construction materials. Concrete, soil, and mulch are ordered by the cubic yard or cubic meter. A cubic excavation 3 m on a side needs 27 m³ of fill — 3³ read straight off the table. Estimators who know the small cubes by heart (up to 10³ = 1,000) can sanity-check supplier quotes mentally.
Cooking and scaling recipes. Scaling a recipe to a larger cube-shaped pan is a cubic relationship: moving from an 8-inch square pan to a 10-inch one multiplies volume by (10/8)³ ≈ 1.95, so you nearly double the batter. Bakers who understand cubing avoid the common error of scaling linearly.
Computer science. Perfect cubes appear in algorithm analysis (O(n³) matrix multiplication), in 3D graphics (voxel grids are n × n × n cubes of data), and in hashing, where cube-based mixing functions spread values. A 100³ voxel grid holds exactly 1,000,000 cells — the 100th perfect cube.
Confusing cubing with multiplying by 3. The single most common error: 5³ is not 15, it is 125. The exponent 3 means “multiply by itself three times,” not “times three.” If your answer to 6³ is 18, stop and recompute: 6 × 6 × 6 = 216.
Mixing up perfect squares and perfect cubes. 64 is both (8² and 4³), but 36 is only a square and 27 is only a cube. When a problem asks for a cube root, the square table will not help — use the cube table.
Assuming every integer near a cube “counts.” Only exact hits are perfect cubes. 1,000 is a perfect cube (10³); 999 and 1,001 are not, even though they are close. Cube roots of non-cubes are irrational — they never terminate or repeat.
Dropping the sign on negative cubes. (−4)³ = −64, not 64. An odd number of negative factors keeps the result negative. The calculator preserves signs automatically, but hand calculations need care with parentheses: −4³ means −(4³) = −64, while (−4)³ is also −64 — here they agree, but the distinction matters for even exponents.
Reading the table backwards. The table maps n → n³. To find ∛(4,913), scan the n³ column for 4,913 and read left: n = 17. Scanning the n column for 4,913 finds nothing and wastes time.
Keep exploring powers and roots: the Cube Calculator cubes any real number including decimals; the Cube Root Calculator inverts the operation for any input; the Exponent Calculator handles arbitrary powers; the Difference of Squares Calculator factors expressions like a² − b²; and the Volume Calculator applies cubing to real three-dimensional shapes.
A perfect cube is an integer of the form n³ for integer n; the first 100 are 1³ through 100³ = 1,000,000. x is a perfect cube iff its cube root is an integer. Consecutive cubes near n differ by approximately 3n². The last digit of a perfect cube uniquely determines the last digit of its integer root. Negative integers have negative perfect cubes since the exponent 3 is odd. Primary uses: cube-root estimation by bracketing, volume computation, and integer sequence reference.
A perfect cube is an integer obtained by cubing another integer — multiplying it by itself three times. Examples include 1 (1³), 8 (2³), 27 (3³), 64 (4³), and 125 (5³). The name comes from geometry: n³ is the volume of a cube with edge length n.
The first 10 perfect cubes are 1, 8, 27, 64, 125, 216, 343, 512, 729, and 1,000 — the cubes of the integers 1 through 10. These ten are worth memorizing because they cover the cube roots most commonly needed in school algebra.
The 100th perfect cube is 1,000,000, since 100³ = 100 × 100 × 100 = 1,000,000 (one million). In general, the nth perfect cube is n³, so round numbers give round results: 20³ = 8,000 and 50³ = 125,000.
Take its cube root: if the result is an integer, the number is a perfect cube. For example, ∛(1,728) = 12 exactly, so 1,728 is a perfect cube; ∛(1,730) ≈ 12.003, not an integer, so 1,730 is not. The calculator on this page performs this test automatically and shows the nearest perfect cubes when the answer is no.
729, which is 9³. Since 10³ = 1,000 exactly, the largest perfect cube strictly below 1,000 is 9³ = 729. Similarly, the largest perfect cube below 100 is 64 (4³), and below 500 it is 343 (7³).
A perfect square is an integer of the form n² (n multiplied by itself twice), while a perfect cube is of the form n³ (three times). The squares begin 1, 4, 9, 16, 25; the cubes begin 1, 8, 27, 64, 125. Some numbers, like 64 (8² = 4³), are both.
Yes to both. 0³ = 0, so zero is a perfect cube, and 1³ = 1, so one is as well. They are the two smallest non-negative perfect cubes, and they are fixed points of cubing: cubing them changes nothing.
Yes. Because 3 is an odd exponent, cubing a negative integer gives a negative result: (−2)³ = −8, (−5)³ = −125, (−10)³ = −1,000. Every negative perfect cube is the negative of a positive one, and its cube root is the corresponding negative integer.
Cite this page as: SigmaCalculator. (2026). First 100 Perfect Cubes. https://sigmacalculator.net/math-calculators/first-100-perfect-cubes/
Last updated: October 9, 2026