Dark-matter halos grown in cosmological simulations appear to have central NFW-like density cusps with mean values of $dlogrho/dlog r approx -1$, and some dispersion, which is generally parametrized by the varying index $alpha$ in the Einasto density profile fitting function. Non-universality in profile shapes is also seen in observed galaxy clusters and possibly dwarf galaxies. Here we show that non-universality, at any given mass scale, is an intrinsic property of DARKexp, a theoretically derived model for collisionless self-gravitating systems. We demonstrate that DARKexp - which has only one shape parameter, $phi_0$ - fits the dispersion in profile shapes of massive simulated halos as well as observed clusters very well. DARKexp also allows for cored dark-matter profiles, such as those found for dwarf spheroidal galaxies. We provide approximate analytical relations between DARKexp $phi_0$, Einasto $alpha$, or the central logarithmic slope in the Dehnen-Tremaine analytical $gamma$-models. The range in halo parameters reflects a substantial variation in the binding energies per unit mass of dark-matter halos.
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