The spatial arrangements and physical properties of one- and two-dimensional structures, based on the amazing cubane (C(8)H(8)) molecule, are investigated in detail. In particular, we compute the electronic structure, both by first principle calculations and by semiempirical methods. The elastic and vibrational properties are evaluated as well. All these results are compared with those of the single cubane molecule, in order to elucidate the influence of dimensionality.