Calculations based on density functional theory (DFT) have been carried out to investigate the electronic and magnetic properties of the alpha -Keggin anions mentioned in the title. The atomic populations and the distribution of the electron density computed for the studied clusters support the hypothesis that an oxidized Keggin anion is an XO4n- clathrate inside a neutral M12O36 cage. The energy gap between the band of occupied orbitals, formally delocalized over the oxo ligands, and the unoccupied d-metal orbitals, delocalized over the addenda, has been found to be independent of the central ion. However, substitution of a W or a Mo by V modifies the relative energy of the LUMO and then induces important changes in the redox properties of the cluster. In agreement with the most recent X-ray determination of [(CoW12O40)-W-III](5-) and with the simplicity of the W-183 NMR and O-17 NMR spectra observed for this anion the calculations suggest that [(CoW12O40)-W-III](5-) has a slightly distorted Td geometry. For the parent cluster [CoW12O40](6-) the quadruplet corresponding to the anion encapsulating a Co-II was found to be similar to1 eV more stable than the species formed by a Co-III and 1 e delocalized over the sphere of tungstens. The one-electron reduction of [(CoW12O40)-W-II](6-) and [(FeW12O40)-W-III](5-) leads to the formation of the 1 e blue species [(CoW12O40)-W-II](7-) and [(FeW12O40)-W-III](6-). The blue-iron cluster is considerably antiferromagnetic, and in full agreement with this behavior the low-spin state computed via a Broken Symmetry approach is 196 cm(-1) lower than the high-spin solution. In contrast, the cobalt blue anion has a low ferromagnetic coupling with an S-T energy gap of +20 cm(-1). This blue species is more stable than the alternative reduction product [(CoW12O40)-W-1](7-) by more than 0.7 eV.