The SERS phenomenon was studied using a large set of silver nanocube dimers programmed to self-assemble in preset locations of a patterned substrate. This SERS substrate made it possible to demonstrate the dependence of the SERS enhancement on the geometry of the silver nanocube dimers and to quantify the dispersion in the SERS enhancement obtained in an ensemble of dimers. In addition to the effects of the gap distance of the dimer and the orientation of the dimer axis relative to the laser polarization on SERS enhancement, the data reveal an interesting dependence of the site-to-site variations of the enhancement on the relative orientation of the nanocubes in the dimer. We observed the highest heterogeneity in the SERS signal intensity with face-to-face dimers and a more robust SERS enhancement with face-to-edge dimers. Numerical calculations indicate that the plasmon resonance frequencies of face-to-face dimers shift considerably with small changes in gap distance. The resonance frequency shifts make it less likely for many of the dimers to satisfy the matching condition between the photon frequencies and the plasmon resonance frequency, offering an explanation for the large site-to-site variations in SERS signal intensity. These results indicate that plasmonic nanostructure designs for SERS substrates for real-world applications should be selected not only to maximize the signal enhancement potential but also to minimize the heterogeneity of the substrate with respect to signal enhancement. The latter criterion poses new challenges to experimentalists and theorists alike.