Problem for the next perfect sqare year!

Algebra Level 3

$\begin{aligned} && 3(1^{2}+4^{2}+9^{2}+16^{2}+\ldots+2025^{2})^{2} \\&&+2(1^{2}+4^{2}+9^{2}+16^{2}+\ldots+2025^{2})+1 \end{aligned}$ Find the remainder when the number above is divided by $(4^{2}+9^{2}+16^{2}+\ldots +2025^{2})$ .