  In resonant inelastic x-ray scattering (RIXS) spectra of K$_2$IrCl$_6$, the
peak for the $j=3/2$ multiplet states shows a splitting that resembles
non-cubic crystal-field effect although the compound is cubic down to 0.3 K.
Here we theoretically describe the RIXS spectra concomitantly treating the
spin-orbit and vibronic interactions. We found that the dynamic Jahn-Teller
effect in the $j=3/2$ multiplet states gives rise to the splitting of the RIXS
spectra and the broadening of the spectra in raising the temperature. The
validity of the interaction parameters for the simulations is supported by our
{\it ab initio} calculations. Our results suggest that, in cubic iridium
compounds, the dynamic Jahn-Teller effect induces the splitting of RIXS spectra
without lowering the symmetry.
