  Calculation of observables with three-dimensional projected entangled pair
states is generally hard, as it requires a contraction of complex multi-layer
tensor networks. We utilize the multi-layer structure of these tensor networks
to largely simplify the contraction. The proposed approach involves the usage
of the layer structure both to simplify the search for the boundary projected
entangled pair states and the single-layer mapping of the final corner transfer
matrix renormalization group contraction. We benchmark our results on the cubic
lattice Heisenberg model, reaching the bond dimension D = 7, and find a good
agreement with the previous results.
