Look! It's A Rectangle!

Geometry

$\Large 12 \times 1^2 + 6 \times 2^2 + 4 \times3^2 + 3\times4^2 = \, ?$

1\times2\times3\times4\times5\times6

1\times2\times3\times4\times5

1\times2\times3\times4

1\times2\times3\times4\times5\times6\times7