The structural stability and electronic properties of the recently characterized three-dimensional (3D) cuboid-shaped C60 polymer are studied using periodic ab initio density functional methods. It is shown that the experimentally observed structure is metastable and not fully relaxed from the high pressure state. A second polymorph, which is more stable than the experimental structure, is identified from the calculations. This new structure differs from the observed structure in the number of fourfold-coordinated atoms per C60 molecule. Both structures are found to be metallic with bulk moduli only about one-third that of diamond. The cuboidal C60 is not the long sought after superhard 3D carbon polymer; however, the two polymorphs studied here reveal unusual electronic band structures that might suggest interesting electronic properties.