Just sum

My derivation is that $a_n = (2n+1)(n^{2})$ , rewritten as $a_n = 2n^{3}+n^{2}$ , then expand the summation into it. Given that $1+8+27+64+\dots+1000000 = 25,502,500$ and $1+4+9+16+\dots+10000 = 338,350$ , plugging in the equation and resolve it would give the answer

I can give a hint If you were not able to solve it:

We can write it as -

$3×1^{2}+5×2^{2}+7×3^{2}+9×4^{2}+11×5^{2}+13×6^{2}+....$

Now we can derive a general sum formula for the above summation-

$=\frac{n(n+1)(3n^{2}+5n+1)}{6}$

Now taking $n=100$ ,

$=\frac{100×101×30501}{6}$

$= \color{#D61F06}{\boxed{51343350}}$

Please give your method to solve this question If you have a different approach( I'm keen to know it. )