  We find by applying MacMahon's partition analysis that all magic labellings
of the cube are of eight types, each generated by six basis elements. A
combinatorial proof of this fact is given. The number of magic labellings of
the cube is thus reobtained as a polynomial in the magic sum of degree $5$.
Then we enumerate magic distinct labellings, the number of which turns out to
be a quasi-polynomial of period 720720. We also find the group of symmetry can
be used to significantly simplify the computation.
