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.
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