In this Letter we study various spin correlated insulating states of F=2 cold
atoms in optical lattices. We find that the effective spin exchange interaction
due to virtual hopping contains an {\em octopole} coupling between two
neighboring lattice sites. Depending on scattering lengths and numbers of
particles per site the ground states are either rotationally invariant dimer or
trimer Mott insulators or insulating states with various spin orders. Three
spin ordered insulating phases are ferromagnetic, cyclic and nematic Mott
insulators. We estimate the phase boundaries for states with different numbers
of atoms per lattice site.Comment: 4 pages, 1 figure include