The 32x32 magic is not only an even multiple of 4, but 4x8 (or 8x4) and that gives many possibilities to construct a 32x32 magic square.
Methodes to construct the 32x32 magic square are:
Symmetric transformation (Liki) and basic key method (ultra magic) leads to ultra magic 32x32 squares, which are panmagic, symmetric, 2x2 compact and each 1/4 row/column gives 1/4 of the magic sum.
Medjig, composite Matroesjka a and b, 30x30 in 32x32, concentric and bimagic are 'specials'.
With the remaining methods you kan construct most perfect (= Franklin pan)magic 32x32 squares.