We study the optical response of clusters of metallic nano-spheres in the electrostatic approximation, using a spherical harmonic representation of the electric field. Using a regular octahedron sphere cluster as an example structure, we investigate field enhancement and near field interactions between the spheres in our cluster. Symmetry properties of the cluster give rise to highly localized peaks in the enhancement of the electric field, denoted as ``hot spots''. From numerical experiments performed at optical frequencies of the incident light, it is found that various geometrical configurations exhibit interesting phenomena; in particular, that field enhancement hot spots move around as the frequency of the incident light changes. To the best of the authors' knowledge, results like these are not found in any previous work.