We perform a first principles investigation of full coupled-cluster doubles and triples (CCDT) calculations on infinite matter consisting of identical fermions using the Minnesota and chiral NNLOopt potentials with a closed shell model and periodic wave functions (Bloch wave functions). We do so with an emphasis on the system energy density as a function of particle number, state space size, and particle density at low to medium densities. Additionally, a CCDT study of the homogeneous electron gas (HEG) is performed. A CCDT programme has been developed with to cope with both memory and cpu consumption, and which can easily be extended to any infinite system, with or without identical fermions. A review of many-body theory and chiral perturbation theory, and also a brief introduction to nuclear forces, is given. We benchmark our data with previous CCD and CCDT-1 results for the HEG, and CCD data for the Minnesota potential. We comment on finite-size effects and wave function boundary conditions with respect to our results, and suggest possible further studies to improve upon our findings.