By the rule for even numbers, the cubes of even numbers are always even.
So, first we have to look for which given numbers are even.
216, 512 and 1000 are the even numbers.
Now, the prime factorization are as follows:
∴ 2 1 6 = 2 × 2 × 2 × 3 × 3 × 3 = 23 × 33 = 63
∴ 5 1 2 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 23 × 23 × 23 = 83
∴ 1000 = 2×2×2×5×5×5 = 23 × 53 = 103
Therefore, we can say that 216, 512 and 1000 are the cube of even numbers.
