Rotated disk electrode voltammetry is described for CH2Cl2 solutions of cluster molecules with nanometersized gold cores and stabilizing ligand shells consisting of mixed monolayers of octanethiolate and omega-ferrocenyloctanethiolate ligands in molar ratios ranging from 2:1 to 24:1. Voltammograms for the cluster molecules exhibit a ferrocene oxidation wave with a limiting current that is under hydrodynamic mass transport control. The current-potential curves preceding ("prewave") and following ("postwave") the ferrocene wave, which are ideally flat, are decidedly sloped. The Delta i/Delta E slopes are proportional to the square root of electrode rotation rate, i.e., are also under hydrodynamic control. The Delta i/Delta E slopes are due to the charging of the electrical double layers of the cluster molecules, showing them to act as diffusing, molecule-sized "nanoelectrodes". A theoretical analysis is presented of the transport control of the double layer charging. Possible reasons that the values of the cluster molecule capacitance (per unit surface area Of cluster molecule, which entails use of models for the shape of the Au core of the cluster) are somewhat larger than the literature expectation for octanethiolate monolayers on flat gold surfaces are discussed. The tiny capacitances of the cluster molecules means that changing their charges by small potential increments can require an average of less than a single electron per cluster molecule.