The 21x21 magic square is odd but also a multiple of 3. You can use the shift method to construct a 21x21 magic square but with boundary conditions. Take as first row of the first and/or second grid 0-1-2-3-4-5-6-7- 8-9-10-11-12-13-14-15-16-17-18-19-20-21and you get only a semi-magic 21x21 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 21x21 square.
 
The row 0-2-1-4-3-5-8-7-6-9-10-11-13-12-14-17-16-15-19-20-18 leads to a valid 21x21 panmagic square, because [yellow marked] 0+4+8+9+13+17+19 = [blue marked] 2+3+7+10+12+16+20 = [pink marked] 1+5+6+11+14+15+18 = 70, that is 1/3 of (0+1+2+3+4+5+6+7+8 +9+10+11+12+13+14+ 15+16+17+18+19+20=) 210.

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

+ 21x number from second grid (shift 2 to the right)

= panmagic 21x21 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