A perfect cube does not end with two zeros

A perfect cube ending with two zeros must be divisible by 100 but not 1000. However, 100 = 2^2 × 5^2. For a cube, each prime exponent must be a multiple of 3. Thus, the smallest cube divisible by 100 is (2×5)^3 = 1000, which ends with three zeros. Any cube divisible by 100 is therefore divisible by 1000, so it ends with at least three zeros. Hence, a perfect cube cannot end with exactly two zeros. The statement is true.