The reduction potentials (E-Red(o) versus SHE) of hypercloso boron hydrides BnHn (n = 6-13) and B12X12 (X = F, Cl, OH, and CH3) in water have been computed using the Conductor-like Polarizable Continuum Model (CPCM) and the Solvation Model Density (SMD) method for solvation modeling. The B3LYP/aug-cc-pvtz and M06-2X/aug-cc-pvtz as well as G4 level of theory were applied to determine the free energies of the first and second electron attachment (Delta G(EA)) to boron clusters. The solvation free energies (Delta G(solv) greatly depend on the choice of the cavity set (UAKS, Pauling, or SMD) while the dependence on the choice of exchange/correlation functional is modest. The SMD cavity set gives the largest Delta Delta G(solv) for BnHn0/- and BnHn-/2- while the UAKS cavity set gives the smallest Delta Delta G(solv) value. The E-Red(o) of BnHn-/2- (n = 6-12) with the G4/M06-2X(Pauling) (energy/solvation(cavity)) combination agrees within 0.2 V of experimental values. The experimental oxidative stability (E-1/2) of BnXn2- (X = F, Cl, OH, and CH3) is usually located between the values predicted using the B3LYP and M06-2X functionals. The disproportionation free energies (Delta G(dpro)) of 2B(n)H(n)(-) -> BnHn + BnHn2- reveal that the stabilities of BnHn- (n = 6-13) to disproportionation decrease in the order B8H8- > B9H9- > B11H11- > B10H10-. The spin densities in B12X12- (X = F, Cl, OH, and CH3) tend to delocalize on the boron atoms rather than on the exterior functional groups. The partitioning of Delta G(solv)(BnHn2-) over spheres allows a rationalization of the nonlinear correlation between Delta G(EA). and E-Red(o) for B6H6-/2-, B11H11-/2-, and B13H13-/2-.