Gas clathrate hydrates solid materials, ubiquitous in the nature as found either on the ocean floor, permafrost on earth or in extraterrestrial planets and comets, are also technologically relevant, e.g., for energy storage or carbon dioxide sequestration. Nitrogen hydrate, in particular, is of great interest as a promoter of the kinetics of methane replacement reaction by carbon dioxide in natural gas hydrates. This hydrate may also appear in the chemistry of planets wherever the nitrogen constitutes the majority of the atmosphere. A fine understanding of the stability of this hydrate under various thermodynamic conditions is thus of utmost importance to assess its role in the many fields where it occurs. In the present work we have investigated the structural properties of the nitrogen hydrate by means of DFT calculations. We show that the lattice parameters strongly depend onto the cage occupancy and that sI structure has higher bulk elasticity than sII structure.An energy analysis reveals the key role played by the cage occupancy onto the type of hydrate structure formed, that could be used for experimentally estimating the cage occupancy through the lattice parameter measurement.