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This proof helps: http://pirate.shu.edu/~wachsmut/ira/infinity/answers/sm_sq_c...

From that: sum bla= n(n+1)(2n+1)/6, then you go distribute

Nice. How did I get the result in the first place?

I know that this sum can be expressed as a cubic polynomial. So I just evaluated the sum at four data-points (n=0,1,2,3) and used those to determine the four coefficents by solving a linear equation system.

Turns out that drawing a picture really helps: http://news.ycombinator.com/item?id=101532

You can usually come up with a clever picture only after you understood the problem - not before.

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