The 15x15 magic square is odd but also a multiple of 3. You can use the shift method to construct a 15x15 magic square but with boundary condition. Take as first row of the first and/or second grid 0-1-2-3-4-5-6-7- 8-9-10-11-12-13-14, than you get only a semi-magic 15x15 square. Take as first row of the first and/or second grid 0-2-1-3-4-5-8-7-6-11-10-9-13-12-14, and you get a panmagic 15x15 square.
 
The row 0-2-1-3-4-5-8-7-6-11-10-9-13-12-14 leads to a valid 15x15 panmagic square because 0+3+8+11+13 = 2+4+7+10+12 = 1+5+6+9+14 = 35, that is 1/3 of (0+1+2+3+4+5+6+7+8 +9+10+11+12+13+14=) 105.

 
 Take 1x number from first grid (shift 2 to the left) +1

+15x number from second grid (shift 2 to the right)

= panmagic 15x15 square

Use the shift method to construct magic squares of odd order from 5x5 to infinity.

See 5x5, 7x7, 9x9 (1), 9x9 (2), 11x11, 13x13, 15x15 (1), 15x15 (2), 17x17, 19x19, 21x21 (1), 21x21 (2), 23x23, 25x25, 27x27 (1), 27x27 (2), 29x29 and 31x31