Answer
See below.
Work Step by Step
We know that the sum of the three solids is $a^3-b^3$ from part a), but using part a), we can only sum them by summing their individual volumes, which gives us the equality: $a^3-b^3=a^2(a-b)+ab(a-b)+b^2(a-b)\\a^3-b^3=(a-b)(a^2+ab+b^2)$
