3D chess do not exist but if we define the bishop to travel parallel to the vector <1, 1, 1> and <1, -1, 1> then the maximum possible number of bishops that could be placed without them threatening each other would be N*N + N*N - 4. N by N bishops will be placed for z = 1 and N by N minus the 4 corners will be placed for z = N.
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