The plasmonic fields of silver and gold nanocubes are known to be among the strongest of any plasmonic metallic nanoparticles. Aggregation dominates their use in imaging and sensing applications due to the resulting enhancement of the plasmonic field in between the nanoparticles (hot spots). The first step in the aggregation process is dimerization. In the present work, we used the discrete dipole approximation (DDA) to calculate the interdimer separation dependence of the absorption and scattering components of the localized surface plasmon resonance (LSPR) extinction of homo and heterodimers of Ag and Au nanocubes when excited parallel to their interparticle axis. We also examined the changes in the nanocube surface plasmonic field distributions as the dimer separation was varied. The results from the homodimers were as expected: as the cubes were brought together, there was a red shift in the primary plasmon band in accordance with the universal scaling law. Additionally, as the particles moved together, scattering contributed more to the overall extinction. By examining the E-field distributions, we found that the hot spot geometry changes abruptly at small separations. At very short distances, the hot spot is located between the adjacent faces and away from the corners of these faces. At larger separations it moves toward the adjacent corners. We observed apparently anomalous behavior for the heterodimer. First, the E-field resulting from excitation of the Ag dominated plasmon resonance was significantly weaker than expected. Second, the red shift of the gold dominated plasmon resonance did not follow the universal scaling law. The most likely explanation for these observations is that the silver plasmon mixes strongly with the energetically resonant, but nonplasmonic, gold interband transition to form a hybrid resonance that produces weaker overall field intensity on the two nanocubes at short separation.