True.
Solution:
On factorising 8640 into prime factors, we got:
8640 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5
On grouping the factors in triples of equal factors, we get:
8640 = {2 × 2 × 2} × {2 × 2 × 2} × {3 × 3 × 3} × 5
It is evident that the prime factors of 8640 cannot be grouped into triples of equal factors such that no factor is left over. Therefore, 8640 is not a perfect cube.