Combinatorial enumeration of colorings of vertices, edges, faces and cells of 4D-hypercubes are considered for all irreducible representations of the 4D-hyperoctahedral group. We have developed computer codes that enumerate colorings of such hypercubes up to 25 dimensions and up to 10 different colors, only limitation being the combinatorial explosion. Tables are obtained for all irreducible representations and colorings for a four-dimensional hypercube with four-colorings. Several applications to spectroscopy, molecular dynamics, boolean algebra, DNA with unnatural pairs, parallel computing and rovibronic states and nuclear spin statistics of non-rigid molecular tetramers such as (H2O)4, (D2O)4, (Cl2O)4, etc., are pointed out.