Put digit 1 in the middle of the top row. Put the digits 2 up to n (= length of the square) each time one cell diagonal up and to the right. Put digit n+1 below digit n. Put the digits n+2 up to 2n each time one cell diagonal up and to the right. Put digit 2n+1 below digit 2n. Etcetera ...

5x5 symmetric magic square

You can use this method to construct magic squares of odd order from 3x3 to infinite and you get symmetric (but not pan)magic squares.