Perfect cubes chart
A perfect cube is a whole number used as a factor three times: 4 × 4 × 4 = 64, so 64 is a perfect cube and 4 is its cube root. This chart lists the cubes of 1 to 20 with their cube roots.
Free printable PDF, 6th grade to 8th grade.
One page, black and white, prints the same every time.
What is on the sheet
| Cube | Cube root |
|---|---|
| 1³ = 1 | ∛1 = 1 |
| 2³ = 8 | ∛8 = 2 |
| 3³ = 27 | ∛27 = 3 |
| 4³ = 64 | ∛64 = 4 |
| 5³ = 125 | ∛125 = 5 |
| 6³ = 216 | ∛216 = 6 |
| 7³ = 343 | ∛343 = 7 |
| 8³ = 512 | ∛512 = 8 |
| 9³ = 729 | ∛729 = 9 |
| 10³ = 1,000 | ∛1,000 = 10 |
| 11³ = 1,331 | ∛1,331 = 11 |
| 12³ = 1,728 | ∛1,728 = 12 |
| 13³ = 2,197 | ∛2,197 = 13 |
| 14³ = 2,744 | ∛2,744 = 14 |
| 15³ = 3,375 | ∛3,375 = 15 |
| 16³ = 4,096 | ∛4,096 = 16 |
| 17³ = 4,913 | ∛4,913 = 17 |
| 18³ = 5,832 | ∛5,832 = 18 |
| 19³ = 6,859 | ∛6,859 = 19 |
| 20³ = 8,000 | ∛8,000 = 20 |
Patterns in the cubes
The last digit of a cube gives away its root. Cubes of numbers ending in 1, 4, 5, 6 and 9 end in the same digit, 2 and 8 swap, and so do 3 and 7: 8³ = 512 ends in 2, and 2³ = 8 ends in 8. With that and the cubes of 1 to 10, a child can find the cube root of any perfect cube up to a million.
The cube of a number ending in 0 ends in three zeros, so 10³ = 1,000 and 20³ = 8,000. The cube of an odd number is odd and the cube of an even number is even.
Where cubes come up
A cube's volume is its side cubed, so a box 3 units on a side holds 27 unit cubes. Sixth grade writes and works out powers like 5³ (CCSS 6.EE.A.1). Eighth grade solves x³ = 64 with a cube root and works out the cube roots of small perfect cubes (8.EE.A.2).
Common questions
- Can a cube root be negative?
- Yes. −4 × −4 × −4 = −64, so the cube root of −64 is −4. Square roots work differently: no real number times itself gives a negative.
- How many perfect cubes are there below 1,000?
- Nine, from 1³ = 1 to 9³ = 729, or ten if you count 0. The next one, 10³, is exactly 1,000.