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This could follow from Gauss' assertion that\[\sum_{i=1}^{n}i=\frac{n(n+1)}{2}\]

i don't remember the details. but i'm pretty sure u can find this in Spivaks' Calculus

It's easy to prove this by induction with your eyes closed, but I'm wondering how it's derived.

Can I provide the link or not here ??

i think this was done in physics section ...

This is nothing but sum of squares of first n natural numbers..

Links are more appreciated than derivations here. ^^

http://www.ilovemaths.com/3sequence.asp
May be it will help you.

http://www.9math.com/book/sum-squares-first-n-natural-numbers
Or you can check this also..

http://www.trans4mind.com/personal_development/mathematics/series/sumNaturalSquares.htm#general_term