  In this work, we study the mass spectrum of the $\Omega_{ccc}$ and
$\Omega_{bbb}$ baryons up to the $N=2$ shell within a nonrelativistic
constituent quark model (NRCQM). The model parameters are adopted from the
determinations by fitting the charmonium and bottomonium spectra in our
previous works. The masses of the $\Omega_{ccc}$ and $\Omega_{bbb}$ baryon
states predicted in present work reasonably agree with the results obtained
with the Lattice QCD calculations. Furthermore, to provide more knowledge of
the $\Omega_{ccc}$ and $\Omega_{bbb}$ states, we evaluate their radiative
decays with the available masses and wave functions from the potential model.
