This paper gives a description of the radiation quality factor and resonances of spherical antennas with material cores. Conditions for cavity and radiating resonances are given, and a theoretical description of the radiation quality factor, as well as simple expressions describing the relative increase in quality factor due to the effect of the internally stored energy are given in special cases. For the air-core antenna of vanishing size, it is shown that the dipole modes are the modes providing the lowest quality factor of all modes. Finally an investigation of the effect of the core permeability and permittivity for an antenna of fixed electrical size is performed.