Cubane, C8H8, can be inserted into the octahedral voids of fullerene lattices to create a family of rotor-stator compounds. We have investigated the structural phase behavior of C60 center dot C8H8 by annealing a number of samples for up to 3 h at selected temperatures in the range 380-870 K under pressures up to 2 GPa. The high-pressure treated materials were then investigated under ambient conditions using Raman spectroscopy and x-ray diffraction. C60 center dot C8H8 is found to have at least five different structural phases depending on treatment conditions. In addition to the known cubic and orthorhombic structures observed at atmospheric pressure, we find two polymeric states with pseudocubic and pseudoorthorhombic structures, respectively, based on the two original lattices and created by heating in different pressure ranges. These materials are believed to be copolymers of C60 and decomposition products of cubane. In contrast to the polymeric states of C60 the present polymer structures are determined by the topology of the original lattices rather than by the molecular structure. Above 700 K we find a carbon-rich amorphous state created when the cubane finally decomposes, releasing its hydrogen content in the form of hydrocarbons.