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Possible Duplicate:
Intuitive explanation for the identity $\sum\limits_{k=1}^n {k^3} = \left(\sum\limits_{k=1}^n k\right)^2$

How to prove this without using mathematical induction?

$1^3+2^3+\cdots+n^3 = (1+2+\cdots+n)^2$

I know how to prove it by induction, is there a different way?

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    @ZevChonoles: But it _is_ a duplicate of both http://math.stackexchange.com/questions/61482/intuitive-explanation-for-the-identity-sum-limits-k-1n-k3-left-sum-l and http://math.stackexchange.com/questions/18548/combinatorial-reasoning-for-the-identity-left-sum-i-1n-i-right-2-l I merged those two together , and perhaps will merge this one since there are useful answers here not yet brought up over there.2012-06-27

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