A cube-free number isn't divisible by \(p^3\) for any prime \(p\) — in its factorization every exponent is 1 or 2. It's the cube analogue of [[squarefree]]. Non-examples are the multiples of a cube: 8, 16, 24, 27, 32, 40, 48, 54.
Cube-free numbers have natural density \(1/\zeta(3) \approx 0.8319\) (about five in six integers are cube-free), where \(\zeta(3)\) is Apéry's constant — the same number Roger Apéry famously proved irrational in 1979.