Vibrational, elastic and dielectric properties of the cubic gauche nitrogen (cg-N) are investigated by analyzing the Raman optic and zone-center phonon modes using the literature data. From the pressure dependence of those Raman modes and the volume data, the isothermal mode Gr?neisen parameter is determined, which increases with the pressure in the cg-N structure. A linear variation is obtained between the Raman frequency shifts and the elastic anharmonicity within the pressure range (0-360 GPa) studied for the cubic gauche nitrogen. Regarding the dielectric properties of the cg-N, frequency dependence of the dielectric permittivity is predicted for the Raman modes at constant pressures and the Cole-Cole plots are constructed for this structure. Our results can be examined by the experimental measurements for the cubic gauche nitrogen when available in the literature.