  We analyze theoretically the emergence of different superfluid phases of
spin-1 bosons in a three-dimensional cubic optical lattice by generalizing the
recently developed Ginzburg-Landau theory for the Bose-Hubbard model to a
spinor Bose gas. In particular at zero temperature, our theory distinguishes
within its validity range between various superfluid phases for an
anti-ferromagnetic interaction with an external magnetic field. In addition, we
determine that the superfluid-Mott insulator phase transition is of second
order and that the transitions between the respective superfluid phases with
anti-ferromagnetic interaction can be both of first and second order.
