What is the sum $\sum_{j=1}^{2n} j^2$? What is the formula to calculate the sum of the following statement?
for example: $$\sum_{j=1}^{n} j^2 = \frac{1}{6}n(n+1)(2n+1)$$
The statement I need help with:
$$\sum_{j=1}^{2n} j^2$$
Thanks for the help in advance, I am really stuck on this question. 

The formula you mentioned itself contains the answer. 
As you know:$\sum_{j=1}^{n} j^2 = \frac{1}{6}n(n+1)(2n+1)$. 
Here on substituting $2n$ in place of $n$ you will get: $$\sum_{j=1}^{2n} j^2=\frac{1}{6}(2n)(2n+1)(4n+1)=\frac{1}{3}n(2n+1)(4n+1)$$
