We investigate the asymptotic formula for the number of representations of a large positive integer as a sum of kth powers of integers represented as the sums of three positive cubes, counted with multiplicities. We also obtain a lower bound for the number of representations when the sums of three cubes are counted without multiplicities.

We show that almost every positive integer can be expressed as a sum of four squares of integers represented as the sums of three positive cubes.

No abstract