What will be the formula of $2^2 + 4^2 + \dots + n^2$?

Question

I'm trying to understand how to calculate $2^2 + 4^2 + \dots + n^2$. I've only succeed to upper bound it by $\dfrac {n^3} 2$. My goal is to say that it is $\Theta (n^3)$.

Thank you

Answer 1

$\textbf{hint}$ your series is $$ \sum_{k=1}^n(2k)^2 = 4\sum_{k=1}^nk^2 = ? $$ (Assuming that its squaring the even numbers - add more terms so we can see what the true series is)