In 5$d^2$ Mott insulators with strong spin-orbit coupling, the lowest pseudospin states form a non-Kramers doublet, which carries quadrupolar and octupolar moments. A family of double-perovskites where magnetic ions form a face-centered cubic (FCC) l
attice, was suggested to unveil an octupolar order offering a rare example in d-orbital systems. The proposed order requires a ferromagnetic octupolar interaction, since the antiferromagnetic (AFM) Ising model is highly frustrated on the FCC lattice. A microscopic model was recently derived for various lattices: for an edge sharing octahedra geometry, AFM Ising octupolar and bond-dependent quadrupolar interactions were found when only dominant inter- and intra-orbital hopping integrals are taken into account. Here we investigate all possible intra- and inter-orbital exchange processes and report that interference of two intra-orbital exchanges generates a ferromagnetic octupolar interaction. Applying the strong-coupling expansion results together with tight binding parameters obtained by density functional theory, we estimate the exchange interactions for the Osmium double-perovskites, Ba$_2$BOsO$_6$ (B = Mg, Ca). Using classical Monte-Carlo simulations, we show these double-perovskites exhibit type-I AFM quadrupolar order followed by an intriguing partial quadrupole order above the transition temperature. Implications of our theory and a way to generate the octupolar order are discussed.
