  The core-cusp problem is one of the controversial issues in the standard
paradigm of $\Lambda$ cold dark matter ($\Lambda$CDM) theory. However, under
the assumption of conventional spherical symmetry, the strong degeneracy among
model parameters makes it unclear whether dwarf spheroidal (dSph) galaxies
indeed have cored dark matter density profiles at the centers. In this work, we
revisit this problem using non-spherical mass models, which have the advantage
of being able to alleviate the degeneracy. Applying our mass models to the
currently available kinematic data of the eight classical dSphs, we find that
within finite uncertainties, most of these dSphs favor cusped central profiles
rather than cored ones. In particular, Draco has a cusped dark matter halo with
high probability even considering a prior bias. We also find the diversity of
the inner slopes in their dark matter halos. To clarify the origin of this
diversity, we investigate the relation between the inner dark matter density
slope and stellar-to-halo mass ratio for the sample dSphs and find this
relation is generally in agreement with the predictions from recent
$\Lambda$CDM and hydrodynamical simulations. We also find that the simulated
subhalos have anti-correlation between the dark matter density at 150 pc and
pericenter distance, which is consistent with the observed one. We estimate
their astrophysical factors for dark matter indirect searches and circular
velocity profiles, associated with huge uncertainties. To more precisely
estimate their dark matter profiles, wide-field spectroscopic surveys for the
dSphs are essential.
