Sum of squares formula, explained only using algebra

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You probably learned 1^2 + 2^2 + ... +n^2= n(n+1)(2n+1)/6
But how did anyone come up with this formula?
In this video, I'll try to explain how it can be derived, only using algebra.
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wow !! i like the way you solve the problems sir, i watched some of ur lectures on fourier . they were soo good . thanks for building maths in me sir.

gorantlakarthik