\(6^2+8^2+10^2+\cdots+102^2\)
\(=\left(2^2+4^2+\cdots+102^2\right)-\left(2^2+4^2\right)\)
\(=2^2\left(1^2+2^2+\cdots+51^2\right)-\left(4+16\right)\)
\(=4\cdot\frac{51\cdot\left(51+1\right)\left(2\cdot51+1\right)}{6}-20=4\cdot\frac{51\cdot52\cdot103}{6}-20\)
=182104-20
=182084