The Dynamical Mean Field Theory (DMFT) maps the lattice problem onto a single site coupled to an electron bath, i.e. the Mean Field. To include spatial correlations we use CDMFT, the cluster extension that connects a cluster of many correlated sites to an electron bath with a matrix-valued hybridization function. Whereas there is only one possible DMFT scheme for the single site, there are different schemes proposed for cluster calculations. They differ in the way they incorporate the lattice symmetry into the cluster calculation done by the impurity solver. We present a comparison of the self-energy and the cumulant periodization for different cluster sizes, applying it to a 1-dimensional chain as well as to the frustrated Kagome lattice. The CDMFT scheme we use is formulated in the real space. We solve the Hubbard cluster impurity model within a Hybridization Expansion Quantum Monte Carlo solver and compare the lattice Green’s function and the local density of states to results of the Density Matrix Renormalization Group method.