Math
Perfect Cube Calculator
Type any whole number to find out if it is a perfect cube.
When it is, you get the exact cube root; when it is not, you see the two perfect cubes it sits between, the distance to each, and the decimal cube root. Negative numbers work because cube roots of negatives are real: -27 = (-3)^3. Switch modes to list every perfect cube between two numbers or to jump straight to the nth perfect cube.
Any whole number up to 60 digits, negatives included. Commas are fine.
Try an example
Result
Perfect cube?
—
- Cube root
- —
- Perfect cube below
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- Perfect cube above
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- Nearest perfect cube
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- Prime factorization
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Study path
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What the perfect cube calculator solves
A perfect cube is an integer equal to some integer multiplied by itself three times: 8 = 2 × 2 × 2, 1728 = 12^3, and -27 = (-3)^3. This calculator tests any integer, returns the exact cube root when there is one, and otherwise shows the two perfect cubes on either side with the decimal cube root. It also lists the perfect cubes in a range and finds the nth cube.
How to recognise a perfect cube
- Take the cube root exactly: the calculator uses integer arithmetic, so a 50-digit number is checked without floating-point error.
- Factor it: every A whole number above 1 whose only factors are 1 and itself. The small raised number saying how many times to multiply the base by itself. must be a multiple of 3. 1728 = 2^6 × 3^3 passes; 500 = 2^2 × 5^3 fails because of the 2^2.
- Use the last digit: cubes can end in any digit, but the last digit of the cube determines the last digit of the root (a cube ending in 2 has a root ending in 8, ending in 3 comes from 7, 7 from 3, 8 from 2, and every other digit maps to itself).
| n | n^3 | Gap to next cube (3n^2 + 3n + 1) |
|---|---|---|
| 1 | 1 | 7 |
| 2 | 8 | 19 |
| 3 | 27 | 37 |
| 5 | 125 | 91 |
| 10 | 1000 | 331 |
| 12 | 1728 | 469 |
| -3 | -27 | 19 (to -8) |
Negative cubes
Unlike squares, cubes keep the sign of their root: (-4)^3 = -64. So negative integers can be perfect cubes, and the cube root of a negative number is a real negative number. On the number line the perfect cubes run …, -64, -27, -8, -1, 0, 1, 8, 27, 64, …
How to use it
- Choose Check one number and type the integer (negatives allowed). Read Yes or No, the cube root, and the neighbouring cubes.
- Choose List perfect cubes in a range to get every r^3 between two numbers with its root.
- Choose Find the nth perfect cube to jump to n^3 with the cubes before and after it.
- Open Show the work for the sandwich estimate, the prime-factorization test, and the exact check.
How to read the answer
Yes means ∛N is an integer and the root shown is exact; for negative N the root is negative. No means N sits strictly between two perfect cubes; the distances show which is nearer and the decimal root shows where ∛N lands. The prime factorization line makes the reason visible: all exponents multiples of 3 means a perfect cube.
Common mistakes and edge cases
- Assuming negatives cannot be perfect cubes. -125 = (-5)^3 is one; only even powers reject negatives.
- Rounding a floating-point cube root: Math.cbrt(1000000000000000001) prints 1000000, hiding the +1. Use exact checks.
- Reading the cube (1728) where the root (12) is wanted, or vice versa.
- Forgetting 0 and 1 are perfect cubes (and -1 too).
- Confusing perfect cubes with perfect squares: 64 is both, 27 is only a cube, 25 is only a square.
Worked examples
Is 1728 a perfect cube?
12^3 = 1728.
Perfect cube?
Yes
Is 100 a perfect cube?
Between 64 and 125.
Perfect cube?
No
Negative perfect cube
-343 = (-7)^3.
Perfect cube?
Yes
Negative non-cube
-30 sits between -64 and -27.
Perfect cube?
No
Zero
0 = 0^3.
Perfect cube?
Yes
Perfect cubes from -100 to 1000
-64 up to 1000.
Perfect cube?
-64, -27, -8, -1, 0, 1, 8, 27, 64, 125, 216, 343, 512, 729, 1,000
12th perfect cube
12^3 = 1728.
Perfect cube?
1,728
Decimal input
Rejected: perfect cubes are integers.
Perfect cube?
Error
Frequently asked questions
What is a perfect cube?+
An integer that equals another integer cubed: 1, 8, 27, 64, 125, … and also 0 and negatives like -8. For example 343 is a perfect cube because 7 × 7 × 7 = 343.
Is 1000 a perfect cube?+
Yes, 10^3 = 1000. Its neighbours are 729 = 9^3 and 1331 = 11^3.
Can a negative number be a perfect cube?+
Yes. (-3)^3 = -27, so -27 is a perfect cube. Odd powers keep the sign of the base.
How do I tell if a number is a perfect cube by hand?+
Estimate the cube root from nearby cubes (10^3 = 1000, 20^3 = 8000), then use the last digit: a cube ending in 8 has a root ending in 2. Check by cubing. Or factor it and see whether every prime exponent is a multiple of 3.
What are the perfect cubes up to 1000?+
1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, the cubes of 1 through 10.
Which numbers are both perfect squares and perfect cubes?+
Perfect sixth powers: 1, 64, 729, 4096, 15625, … since r^6 = (r^3)^2 = (r^2)^3.
About this calculator
- Written by
- mathcheck editorial team
- Last reviewed
- September 4, 2026
Method
- Uses the values entered by the user and stable formulas documented on the page.
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Last updated: September 4, 2026