The molecular cubic-block model [ J. Chem. Phys. 2005, 123, 164904 ] is used to study a class of poly(benzyl ether) fullerodendrimers that have recently been reported to form columnar liquid crystal phases. In agreement with experiment, the model-molecules are found to self-assemble into columns which form hexagonal or rectangular lattices. The columnar cross sections are elongated in the rectangular phase. Transitions to the isotropic phase, either directly or through the intermediate formation of smectic phases, have been found. The effects of dissolving small amounts of nonbonded fullerene molecules have been explored. The results predict that the fullerene solutes restrict the range of stability of the columnar phase and may induce transitions from the columnar to the smectic or the isotropic phase.