Sum of the first odd squares

Statement

Compute the sum of the first four odd squares $1^2+3^2+5^2+7^2$ and check it is a tetrahedral number.

Solution

$1^2+3^2+5^2+7^2=1+9+25+49=\boxed{84}.$ This is $\mathrm{Tet}_7=\dfrac{7\cdot 8\cdot 9}{6}=84$: the sum of the first $n$ odd squares is always the tetrahedral number $\mathrm{Tet}_{2n-1}$ (here $n=4$, $2n-1=7$).