A magic square consists of the numbers $1,2,\ldots,m^2$ placed into $m\times m$ square grid, so that every row, column, and both diagonals have the same sum. The magic constant of the square is this common sum.
Based on the dimensions of an $m\times m$ square, can you determine what the magic constant is? If so, how can you do that? If not, please explain why it isn't possible.
For example, here are some magic square "magic constants";
$1\times 1\,\to\, 1 $
$2\times 2 \,\to nil$
$3\times 3\,\to \,15$
$5\times 5 \,\to\, 65$
How can you determine the $6\times 6$, $7\times7$, etc. just from the dimensions?
Please note; I'm not asking for how to solve an $m\times m$ magic square, nor do I want a "trial and error" answer. I want a mathematical based answer explaining how to figure out the magic constant of a magic square with the dimensions $m\times m$.