Every cube from 1³ to 20³, their cube roots, and the patterns that make them easy to remember
A cube number is a number multiplied by itself three times: 4³ = 4 × 4 × 4 = 64. The first ten cube numbers are 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000.
Read the table either way: 12³ = 1,728, so the cube root of 1,728 is 12.
| n | n³ | Working |
|---|---|---|
| 1 | 1 | 1 × 1 × 1 |
| 2 | 8 | 2 × 2 × 2 |
| 3 | 27 | 3 × 3 × 3 |
| 4 | 64 | 4 × 4 × 4 |
| 5 | 125 | 5 × 5 × 5 |
| 6 | 216 | 6 × 6 × 6 |
| 7 | 343 | 7 × 7 × 7 |
| 8 | 512 | 8 × 8 × 8 |
| 9 | 729 | 9 × 9 × 9 |
| 10 | 1,000 | 10 × 10 × 10 |
| 11 | 1,331 | 11 × 11 × 11 |
| 12 | 1,728 | 12 × 12 × 12 |
| 13 | 2,197 | 13 × 13 × 13 |
| 14 | 2,744 | 14 × 14 × 14 |
| 15 | 3,375 | 15 × 15 × 15 |
| 16 | 4,096 | 16 × 16 × 16 |
| 17 | 4,913 | 17 × 17 × 17 |
| 18 | 5,832 | 18 × 18 × 18 |
| 19 | 6,859 | 19 × 19 × 19 |
| 20 | 8,000 | 20 × 20 × 20 |
Every digit 0–9 appears exactly once as the last digit of a cube, so the last digit of a cube tells you the last digit of its root. 1, 4, 5, 6, 9 and 0 keep their own ending (4³ = 64, 9³ = 729). The others swap in pairs: 2 ↔ 8 (2³ = 8, 8³ = 512) and 3 ↔ 7 (3³ = 27, 7³ = 343).
That makes perfect cube roots a two-step job. For perfect cubes up to a million: the last digit gives the root's last digit, and the thousands give its first digit. 175,616 ends in 6, so the root ends in 6; 175 sits between 125 = 5³ and 216 = 6³, so the root starts with 5. The answer is 56.
A square is a number times itself (area of a square); a cube is a number times itself times itself (volume of a cube). 1 and 64 are the only numbers under 100 that are both — 64 is 8² and 4³. The next is 729 = 27² = 9³.
Cubes grow fast: 10³ is a thousand, 100³ a million. A box twice as wide, deep and tall holds 2³ = 8 times as much, which is why doubling a recipe's pan size is never just double the batter.
Bracket it between neighbouring cubes. The cube root of 100 sits between 4 (64) and 5 (125), a little past halfway, so about 4.6 — the true value is 4.642. For 500: between 7 (343) and 8 (512), very close to 8, so just under 8 — actually 7.937.
1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125, 6³ = 216, 7³ = 343, 8³ = 512, 9³ = 729, 10³ = 1000.
10, because 10 × 10 × 10 = 1,000.
Both. 64 = 8 × 8 = 8², and 64 = 4 × 4 × 4 = 4³. It is the smallest number above 1 that is a square and a cube.
Yes. (−3)³ = −27, because a negative multiplied three times stays negative. So the cube root of −27 is −3, unlike square roots of negatives.
Square numbers are on their own page, and the exponent calculator works out any power with the working shown.