Induction and formulating equations

While browsing, I came across equations for finding the sums of certain series's, the first is (n²+n)/2 for "1+2+3...+n", the second is (1/6)n(n+1)(2n+1) for "1²+2²+3²...n²".

I found out how to come up with the first equation through reasoning: n(n+1)/2 is basically the median times n, and since the difference in this series is 1, and the series begins with 1, the median is the same as the mean, so the mean times the number of numbers in the series finds the total.

Now what I can't figure out is how to formulate the second equation, any ideas?