(i) The prime factorisation of 216 is as follows.

216 = __2 × 2 × 2__ × __3 × 3 × 3__ = 2^{3} × 3^{3}

Here, as each prime factor is appearing as many times as a perfect multiple of 3, therefore, 216 is a perfect cube.

(ii)The prime factorisation of 128 is as follows.

128 = __2 × 2 × 2__ × __2 × 2 × 2__ × 2

Here, each prime factor is not appearing as many times as a perfect multiple of 3. One 2 is remaining after grouping the triplets of 2. Therefore, 128 is not a perfect cube.

(iii) The prime factorisation of 1000 is as follows

1000 = __2 × 2 × 2__ ×__ 5 × 5 × 5__

Here, as each prime factor is appearing as many times as a perfect multiple of 3, therefore, 1000 is a perfect cube.