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ABSTRACT We analyse the cold dark matter density profiles of 54 galaxy haloes simulated with Feedback In Realistic Environments (FIRE)-2 galaxy formation physics, each resolved within $$0.5{{\ \rm per\ cent}}$$ of the halo virial radius. These haloes contain galaxies with masses that range from ultrafaint dwarfs ($$M_\star \simeq 10^{4.5}\, \mathrm{M}_{\odot }$$) to the largest spirals ($$M_\star \simeq 10^{11}\, \mathrm{M}_{\odot }$$) and have density profiles that are both cored and cuspy. We characterize our results using a new, analytic density profile that extends the standard two-parameter Einasto form to allow for a pronounced constant density core in the resolved innermost radius. With one additional core-radius parameter, rc, this three-parameter core-Einasto profile is able to characterize our feedback-impacted dark matter haloes more accurately than other three-parameter profiles proposed in the literature. To enable comparisons with observations, we provide fitting functions for rc and other profile parameters as a function of both M⋆ and M⋆/Mhalo. In agreement with past studies, we find that dark matter core formation is most efficient at the characteristic stellar-to-halo mass ratio M⋆/Mhalo ≃ 5 × 10−3, or $$M_{\star } \sim 10^9 \, \mathrm{M}_{\odot }$$, with cores that are roughly the size of the galaxy half-light radius, rc ≃ 1−5 kpc. Furthermore, we find no evidence for core formation at radii $$\gtrsim 100\ \rm pc$$ in galaxies with M⋆/Mhalo < 5 × 10−4 or $$M_\star \lesssim 10^6 \, \mathrm{M}_{\odot }$$. For Milky Way-size galaxies, baryonic contraction often makes haloes significantly more concentrated and dense at the stellar half-light radius than DMO runs. However, even at the Milky Way scale, FIRE-2 galaxy formation still produces small dark matter cores of ≃ 0.5−2 kpc in size. Recent evidence for a ∼2 kpc core in the Milky Way’s dark matter halo is consistent with this expectation.