  We study itinerant ferromagnetism in a $t_{2g}$ multi-orbital Hubbard system
in the cubic lattice, which consists of three planar oriented orbital bands of
$d_{xy}$, $d_{yz}$, and $d_{zx}$. Electrons in each orbital band can only move
within a two-dimensional plane in the three-dimensional lattice parallel to the
corresponding orbital orientation. Electrons of different orbitals interact
through the on-site multi-orbital interactions including Hund's coupling. The
strong coupling limit is considered in which there are no doubly occupied
orbitals but multiple on-site occupations are allowed. We show that, in the
case in which there is one and only one hole for each orbital band in each
layer parallel to the orbital orientation, the ground state is a fully
spin-polarized itinerant ferromagnetic state, which is unique apart from the
trivial spin degeneracy. When the lattice is reduced into a single
two-dimensional layer, the $d_{zx}$ and $d_{yz}$ bands become
quasi-one-dimensional while the $d_{xy}$ band remains two-dimensional. The
ground state ferromagnetism also appears in the strong-coupling limit as a
generalization of the double exchange mechanism. Possible applications to the
systems of SrRuO$_3$ and LaAlO$_3$/SrTiO$_3$ interface are discussed.
