I have a question.
What exactly would happen if you changed e=mc2 to e=mc3?
The pedantic answer is that you would would wreck the equation.
I think the reason "c" is squared is because the whole equation is related to the equation E=1/2 Mv^2, where the constant "c" (the speed of light) is a special velocity.
More deeply, I think velocity is squared because velocity is a function of distance over time, which are two dimensions and thus represented by squaring (^2).
Perhaps someone more literate in math can explain it better than that.