The structure and properties of cubic spinel nitrides were investigated based on first-principles theoretical calculations. The lattice constants, bulk moduli, band structures, electronic bonding, and lattice stability of thirty-nine single and double nitrides were studied. The single spinel nitrides of the form c-A(3)N(4) (where A is a Group IVA element), except c-Hf3N4, are all semiconductors with band gaps ranging from an indirect gap of 0.07 eV in c-Ti3N4 to a direct gap of 3.45 eV in c-Si3N4. For double nitrides of the form c-AB(2)N(4) (where A and B are Group IVA (Ti, Zr, Hf) or IVB (C, Si, Ge, Sri) elements), both metallic and insulating band structures are possible. The stability of the double spinel nitrides, relative to single nitrides, is dependent on the optimal cation radii and polyhedral volumes at the tetrahedral A sites and the octahedral B sites. Of the thirty-two double nitrides, only nine are predicted to be energetically favorable. Among the potentially stable phases, the most interesting ones are c-CSi2N4 (which has an exceptionally strong covalent bonding and large bulk modulus), c-SiGe2N4 (which has an energetically favorable direct band gap of 1.85 eV), and c-SiTi2N4 (which is metallic).