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

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