A sharp and intense structure of the core exciton is observed in total photon yield spectra of a cubic BN crystal at 192 eV, below the transition from the boron 1s level to the conduction-band edge. We have discovered, however, that the Raman intensity for leaving behind the valence exciton does not show any enhancement even when the frequency of the incident field crosses the core-exciton level. This comes from the fact that relative magnitudes among the nonlinear channels depend on the relevant frequency. We analyzed the Raman spectra taking into account the strong coupling between the core exciton and radiation fields, i.e., the polariton effect, Rayleigh scattering, and the Auger process. ͓S0163-1829͑97͒09335-1͔