Compilation of proofs for the summation of natural squares and cubes – math.stackexchange.com

Compilation of proofs for the summation of natural squares and cubes – math.stackexchange.com

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I want to know different proofs for the following formulas, $$ \sum_{i=1}^n{i^2} = \frac{(n)(n+1)(2n+1)}{6} $$ $$ \sum_{i=1}^n{i^3} = \frac{n^2(n+1)^2}{2^2} $$ Please do not mark this as duplicate, ...

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