Ground and excited electronic states of neutral, cationic and anionic germanium and tin hexamers (Ge-6 and Sn-6) are investigated. Different geometries such as tetragonal bipyramid (D-4h,D-2h) and edge-caped trigonal bipyramid (C-2v) (ECTBP) were studied. We have employed a number of high level electron correlation techniques such as large scale multireference singles+doubles configuration interaction (MRSDCI) computations that included up to 16 million configurations, complete active-space multiconfiguration self-consistent filed (CAS-MCSCF), and Moller-Plesset (MP2) techniques to investigate the low-lying electronic states, their geometries and energy separations. A (1)A(1g) tetragonal bipyramid structure (D-4h symmetry) is found as the ground state for both Ge-6 and Sn-6, in accord with the previously suggested experimental assignments. The excitation energies, atomization energies, ionization potentials and vertical and adiabatic electron affinities are computed and compared with the experimental results. Our computations of the excited states of these species have facilitated assignment of the anion photodetachment spectra of the anions of these clusters and comparison with the photoionization spectra of the neutral species.