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We report a theoretical investigation of temperature, size, and composition effects on the structural, energetic, and electronic properties of the (La4O6)n, (La2Ce2O7)n, and (Ce4O8)n nanoclusters (NCs) for n = 10, 18. Furthermore, we investigated the single O vacancy formation energy as a function of the geometric location within the NC. Our calculations are based on the combination of force-field molecular dynamics (MD) simulations and density functional theory calculations. We identified a phase transition from disordered to ordered structures for all NCs via MD simulations and structural analysis, e.g., radius changes, radial distribution function, common neighbor analysis, etc. The transition is sharp for La36Ce36O126, La20Ce20O70, and Ce72O144 due to the crystalline domains in the core and less abrupt for Ce40O80, La40O60, and La72O108. As expected, radius changes are abrupt at the transition temperature, as are morphological differences between NCs located below and above the transition temperature. We found a strong dependence on the O vacancy formation energy (Evac) and its location within the NCs. For example, for La40O60, Evac decreases almost linearly as the distance from the geometric center increases; however, the same trend was not observed for Ce40O80, while there are large deviations from the linear trend for La20Ce20O70. Evac has smaller values for Ce40O80 and higher values for La40O60, that is, almost three times, while Evac has intermediate values for mixed oxides, as expected from weighted averages. Therefore, the mixture of one formula unit of La2O3 with two formula units of CeO2 has the effect of increasing the stability of CeO2 (binding energy), which increases the magnitude of the formation energy of the O vacancy. [ABSTRACT FROM AUTHOR]