Put number 1 in the middle of the top row. Put the numbers 2 up to n (= lenght of the square) each time (using a chess knight movement) 1 cell to the right and 2 cells down. Put number n+1 below number n. Put the numbers n+2 up to 2n each time 1 cell to the right and 2 cells down. Put number 2n+1 below number 2n. Etcetera ...

Put digit 1 up to 7 and 8 in the square         7x7 symmetric magic square

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

See 3x3, 5x5, 7x7, 9x9, 11x11, 13x13, 15x15, 17x17, 19x19, 21x21, 23x23, 25x25, 27x27,  29x29 and 31x31