Prove that 1^3 + 2^3 + · · · + n^3 = (1 + 2 + · · · + n)^2 forevery n ? N. That is, the sum of the first n perfect cubes is thesquare of the sum of the first n natural numbers. (As a student, Ifound it very surprising that the sum of the first n perfect cubeswas always a perfect square at all.)
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