In this video I continue on my summation proofs series and show the proof for determining the formula for the sum of the cubes of "n" consecutive integers, i.e. 1³ + 2³ + 3³ +.... + n³. This is a similar proof to my sum of squares proof (see video link below) and involves the use of the useful "telescoping" or collapsing sum which I illustrate in the video.

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Sum of the Cubes of "n" Consecutive integers

Simple Proof

We start off the proof with the “telescoping sum” (or the collapsing sum):

Example