Cubic heterostructured (BA) particles of Prussian blue analogues, composed of a shell of ferromagnetic K_{0.3}Ni[Cr(CN)_6]_{0.8} cdot 1.3H_2O (A), Tc ~ 70 K, surrounding a bulk core of photoactive ferrimagnetic Rb_{0.4}Co[Fe(CN)_6]_{0.8} cdot 1.2H_2O (B), Tc ~20 K, have been studied. Below Tc ~ 70 K, these samples exhibit a persistent photoinduced decrease in low-field magnetization, and these results resemble data from other core-shell particles and analogous ABA heterostructured films. This net decrease suggests that the photoinduced lattice expansion in the B layer generates a strain-induced decrease in the magnetization of the A layer, similar to a pressure-induced decrease observed by others in a pure A-like material and by us in our BA cubes. Upon further examination, the data also reveal a significant portion of the A material whose superexchange, J, is perturbed by the photoinduced strain from the B constituent.