Let n=k,12+22+32+42+52+62+...+k 2 = k (k+1) (2k+1)/6.

Then when n=k+ 1, 1 2+3 2+4 2+5 2+6 2+ ... +k 2+(k+ 1) 2 = k (k+66

=(2k^2+7k+6)(k+ 1)/6=(2k+3)(k+2)(k+ 1)/6

So ... . . .