Problem for the next perfect sqare year!

Algebra Level 3

3(12+42+92+162++20252)2+2(12+42+92+162++20252)+1 \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 (42+92+162++20252)(4^{2}+9^{2}+16^{2}+\ldots +2025^{2}).

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