Try solving these

remember that this is a square equation but not x^2 only

Couldn't the sum of squares be expressed also as the volume of a pyramid having a square base?

So sum(x=1,x<=n,x++) is a pyramid with base n^2 and height n, meaning volume 

S=(1/3)(n^2)(n)=n^3/3.

What did I do wrong here?

ColdCoffee's answer of 402636 is correct (checked it with Mathematica.)

yep