The sum of the consecutive integers from 1 to n is (n/2)(n+1), as discovered (I think) by Gauss a long time ago.

The sum of the cubes of consecutive integers from 1 to n is the square of the result above.

My question is why does this result happen??

To clarify - I am 100% the result is true - proving either result by induction is a standard question for my A Level Mathematicians, and the Gauss proof is a great introduction to proof for younger students.

What I'd like to find is a geometric argument for why they are the same, rather than an algebraic one.﻿
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