A ‘trick’ to construct the 3x3 magic square is the diagonal method of Yang Hui:
3x3 magic square
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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.
See 3x3, 5x5, 7x7, 9x9, 11x11, 13x13, 15x15, 17x17, 19x19, 21x21, 23x23, 25x25, 27x27, 29x29 and 31x31