[Medjig method] I have used the Medjig method 3D to construct a Nasik (= pandiagonal & pantriagonal) 16x16x16 magic cube and 1/2 rows/columns/diagonals in each level give 1/2 of the magic sum.
[Knight jump method] René Chrétien created a Nasik 16x16x16 magic cube. You can find sequential numbers in the magic cube by using chess knight jumps.
Construct a Franklin panmagic 16x16x16 cube. This cube must be 2x2(x2) compact and 1/2 rows/columns/diagonals in the levels and 1/2 space diagonals must give 1/2 of the magic sum.
[Composite 1a] Use a 8x8x8 Franklin panmagic square to construct a Franklin panmagic 16x16x16 cube (1)
[Composite 1b] Use a 4x4 panmagic square to construct a Franklin panmagic 16x16x16 cube (2)
[Composite 2] Use Dwane Campbell's 8x8x8 magic cube to construct a Franklin panmagic 16x16x16 cube (3).
N.B.: Whizz kids say that only the first and the third version are valid Franklin panmagic 16x16x16 cubes, because it consists of 8 proportional Nasik 8x8x8 magic cubes.