Simulations predict that the dark matter halos of galaxies should have central cusps, while those inferred from observed galaxies do not have cusps. We demonstrate, using both linear perturbation theory and n-body simulations, that a disk bar, which should be ubiquitous in forming galaxies, can produce cores in cuspy cold dark matter profiles within five bar orbital times. Simulations of forming galaxies suggest that one of Milky Way size could have a 10 kpc primordial bar; this bar will remove the cusp out to ~2.5 kpc in ~1.5 Gyr, while the disk would lose only ~8% of its original angular momentum. Larger bars would remove the cusp out to correspondingly larger radii. An inner Lindblad-like resonance couples the rotating bar to orbits at all radii through the cusp, transferring the bar-pattern angular momentum to the dark matter cusp, rapidly flattening it. This resonance disappears for profiles with cores and is responsible for a qualitative difference in bar-driven halo evolution with and without a cusp. This bar-induced evolution will have a profound effect on the structure and evolution of almost all galaxies. Hence, both to understand galaxy formation and evolution and to make predictions from theory, it is necessary to resolve these dynamical processes. Unfortunately, correctly resolving these important dynamical processes in ab initio calculations of galaxy formation is a daunting task, requiring at least 4,000,000 halo particles using our SCF code and probably requiring many times more particles when using noisier tree, direct summation, or grid-based techniques—the usual methods employed in such calculations.