The cubic Prussian blue analogue Mn₃[Mn(CN)₆]₂ · 15 H₂O, which has the advantage of being transparent and magnetic (T_N = 35 K) at the same time, has been investigated by density functional theory (DFT) calculations. The three-dimensional structure is built of Mn^II ions linked to Mn^III ions by μ-bridging cyanides, to form a crystal structure, which is related to the NaCl type. In a first step, the relative stabilities of the mononuclear complexes [Mn(CN)₆]^z- (z = 2 to 4) have been studied as a function of the oxidation state, spin configuration, and the linkage isomerism of the cyanide ligand. The results we have obtained by this investigation are in good agreement with our chemical expertise. In addition, the calculations have been extended to the dinuclear [Mn₂(CN)₁₁]^z- (z = 5 and 6) clusters. Furthermore, we used DFT to model the magnetic properties as well as the ³T₁ → ¹T₂ transition, which has been observed by single-crystal near-IR spectra of Mn₃[Mn(CN)₆]₂ · 15 H₂O.