Among transition-metal nitrides, the mononitride cubic-MoN with a rock-salt structure has drawn particular attention because it has been predicted to possess excellent mechanical and electronic properties, especially the high superconducting temperature around 30 K. However, synthesis of bulk cubic-MoNx with the nitrogen concentration, x, more than 0.5 is still challenging, leading to contradictions on its phase stability and properties. In this work, we formulated a high-pressure synthesis reaction for the formation of single-crystal cubic-MoNx with a remarkably high nitrogen concentration value of x≈0.67. This nitride possesses a high asymptotic hardness of 24 GPa, which is so far the second hardest among metal nitrides. Impressively, the expected superconductivity is absent in the as-synthesized product. We further performed density functional theory calculations to clarify the structural stability and the absence of superconductivity in stoichiometric cubic-MoN. We find that the ground state of cubic-MoN is theoretically explored to be a Mott insulator with an antiferromagnetic phase, while a paramagnetic configuration is adopted at the ambient conditions. Such magnetic properties would explain the structural stability and the absence of superconductivity in the as-synthesized cubic-MoNx with a high nitrogen concentration.