We have obtained the energy spectra of cosmic ray He, B, C, O, Mg, S and Fe nuclei in the range 0.5-1.5 GeV/nuc and above using the penetrating particle mode of the High Energy Telescope, part of the Cosmic Ray Science (CRS) experiment on Voyagers 1 and 2. The data analysis procedures are the same as those used to obtain similar spectra from the identical V2 HET telescope while it was in the heliosphere between about 23 and 54 AU. The time period of analysis includes 4 years of data beyond the heliopause (HP). These new interstellar spectra are compared with various earlier experiments at the same energies at the Earth to determine the solar modulation parameter, phi. These new spectra are also compared with recent measurements of the spectra of the same nuclei measured by the same telescope at low energies. It is found that the ratio of intensities at 100 MeV/nuc to those at 1.0 GeV/nuc are significantly Z dependent. Some of this Z dependence can be explained by the Z2 dependence of energy loss by ionization in the 7-10 g/cm2 of interstellar H and He traversed by cosmic rays of these energies in the galaxy; some by the Z dependent loss due to nuclear interactions in this same material; some by possible differences in the source spectra of these nuclei and some by the non-uniformity of the source distribution and propagation conditions. The observed features of the spectra, also including a Z dependence of the peak intensities of the various nuclei, pose interesting problems related to the propagation and source distribution of these cosmic rays.