Candidates for the lowest energy structures of medium-sized Au-n, n = 32, 38, 44, 50, and 56, clusters were evaluated using gradient-corrected DFT computations. Both hollow cage and space-filling conformations were considered. The cages were constructed using fullerene-based templates. The space-filling structures were generated by employing a genetic algorithm. We have found that the space-filling isomers were lower in energy except for two notable cases. Like Au-32 [Johansson, M. P.; Sundholm, D.; Vaara, J. Angew. Chem. Int. Ed. 2004, 43, 2678], a hollow cage configuration of Au-50 is more stable than its alternative space-filling isomeric forms. The unusual stabilities of the cage Au-32 and Au-50 can be attributed to spherical aromaticity; both exhibit large negative nucleus-independent chemical shifts and exceptionally large HOMO-LUMO gaps.