We have calculated the geometrical structure, relative stability, and nitrogen chemical shifts of five boron nitride hollow octahedral cages using density functional theory. Our results show three typical ranges for nitrogen chemical shifts corresponding to each of the nonequivalent magnetic sites of the N atoms. The principal component of the electric field gradient tensor at each N-14 site in boron nitride cages is predicted to be much smaller than the corresponding value in borazine, which should reflect in sharper spectral lines and much better resolution.