How this calculator works
A perfect cube is a whole number that equals another whole number raised to the third power. Because an odd power keeps the sign, negative numbers can be perfect cubes while negative numbers can never be perfect squares. The integer cube root is found with exact integer arithmetic, then cubed and compared with the input, so no floating-point estimate is involved.
Formula
n is a perfect cube when n = k^3 for an integer k. For n ≥ 0 the integer cube root is the largest k with k^3 ≤ n; for n < 0 the same search runs on |n| and the answer is negated.
Worked example
27 = 3^3 and -8 = (-2)^3, so both are perfect cubes. The number 30 is not: it lies between 27 (3^3) and 64 (4^3).
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Frequently asked questions
Can a negative number be a perfect cube?
Yes. (-2)^3 = -8 and (-5)^3 = -125. Odd powers preserve the negative sign, which is why this calculator accepts negatives while the perfect square page does not.
What are the first perfect cubes?
Starting from zero they are 0, 1, 8, 27, 64, 125, 216, 343, 512 and 729. The differences between consecutive cubes grow quickly: each step adds 3k^2 + 3k + 1.
Why is the integer cube root rounded down?
Rounding down gives the largest whole cube that does not exceed the input. For a perfect cube it is exactly the cube root; for other inputs it is the lower neighbour, and the upper neighbour is one more.