Use an ultra magic 15x15 square to construct a 15x15x15x15 magic cube. Construct the first grid by placing the 15x15 magic square in the middle level of the middle (3D-)cube. Create by shift-2 in the rows and columns 225 different shifted versions of the 15x15 magic square, filling the 15x15x15x15 magic cube. Construct the second grid by using shift-2 in the opposite direction.
The 15x15x15x15 magic cube is pantriagonal & panquadragonal magic, panmagic in the levels and 1/2 pandiagonal magic through the levels. So the 15x15x15x15 magic cube misses 1/2 magic feature to be Nasik perfect. The cube is also symmetric and each level is 3x3 and 5x5 compact.
N.B.: The smallest four dimensional Nasik perfect magic cube is the 16x16x16x16 magic cube.
See for grids, the result and the check (if all numbers are in the magic cube and addition of the numbers give the right magic sum) the download below.