We have investigated the merging of galaxies with central, massive black holes. We performed simulations of hierarchical mergings, in which the merger remnant of one simulation is used as the progenitor for the next simulation. Our main results are the following: First, the central part of the merger has a very shallow density cusp (ρ is proportional to r^-α^, with α <~ 51). This result is in good agreement with recent Hubble Space Telescope results that suggest most large elliptical galaxies have shallow density cusps. This shallow cusp yields an almost constant surface density. The radius of this shallow cusp (core) roughly doubles at each merger event. This expansion of the core is supported by the energy production from the black hole binary. As a result, the ratio between the core radius and the half-mass radius remains roughly constant. This result is, again, in good agreement with the observed positive correlation between the core radius and effective radius of elliptical galaxies. In previous simulations of galactic mergers, the role of the central black holes was neglected. In these simulations, the half-mass radius increased but the core radius did not, in clear disagreement with observations. Our results imply that the existence of central black holes naturally explains the structure and size of the cores of bright elliptical galaxies, though other explanations (e.g., anisotropy) are not ruled out.