The charge-transfer band gap of the iron cyanide framework material Prussian Blue and its dependence on the type and location of the charge-compensating interstitial cations (K+, Rb+, Cs+) are investigated via periodic density functional (DF) calculations. The calculated variation in the band gap magnitude with respect to cation type confirms recent experimental results on cation-induced spectral shifts. The role of both the cation interaction with the framework and the cation-induced lattice expansion are examined with respect to their influence on the band gap. The gap magnitude is related to the cation type but is found to be more strongly affected by cation-induced lattice distortion as the cation passes through the material. Our results support the possibility of engineering the electronic structure of Prussian Blue type materials through guest-induced host-framework distortion.