Which of the following is NOT a perfect cube?

Which of the following is NOT a perfect cube?
  1. $8$
  2. $27$
  3. $100$
  4. $125$

Solution

$8 = 2^{3}$, $27 = 3^{3}$, $125 = 5^{3}$. But $4^{3} = 64$ and $5^{3} = 125$, so $100$ is not a perfect cube.

Asked in: IMO

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