## Combinatorics - Mathematical Induction?

Hello, I am having trouble solving this problem. Maybe I'm just overreacting to it. In my two semesters in discrete math/combinatorics, I've never seen a problem like this (with two summations) and been asked to prove it. Can some one help?

$\sum^{n}_{i=1} i^3 = \frac{n^2(n+1)^2}{4} = (\sum^{n}_{i=1} i)^2$

I mean, I know the whole S(n), S(1), S(k), S(k+1) steps, but I'm just unsure of how to write it. The solutions manual for the book skip that problem.

Book: Discrete And Combinatorial Mathematics: An Applied Introduction by Ralph P. Grimaldi, 5th Edition.

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