Hyper-Raman scattering of cubic zirconia and ${\mathrm{CaF}}_{2}$ is measured at room temperature. For a ${\mathrm{CaF}}_{2}$ crystal, the frequencies of the TO and LO modes with ${T}_{1u}$ symmetry are determined to be 260 and 480 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, which are in good accord with the results of infrared measurements. In a fluorite-type cubic zirconia, the defect-induced hyper-Raman spectra due to the oxygen vacancies are observed. The structures of the hyper-Raman spectra are reasonably explained by the frequency distribution of hyper-Raman-active modes in the whole Brillouin zone, which is estimated from the imaginary part of the simple projections of the phonon displacement-displacement Green's functions onto a defect space consisting of an ${\mathrm{O}}_{6}$ molecule. From the analysis of the mode vectors for the ${\mathrm{O}}_{6}$ molecule, the attempt frequency of oxygen ions is found to correspond to the 690-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ band in the observed hyper-Raman spectra with ${T}_{1u}$ symmetry.