The electronic structure and properties of cerium oxides ($\mathrm{Ce}{\mathrm{O}}_2$ and ${\mathrm{Ce}}_2{\mathrm{O}}_3$) have been studied in the framework of the $\mathrm{LDA}+\mathrm{U}$ and $\mathrm{GGA}\left(\mathrm{PW}91\right)+\mathrm{U}$ implementations of density functional theory. The dependence of selected observables of these materials on the effective U parameter has been investigated in detail. The examined properties include lattice constants, bulk moduli, density of states, and formation energies of $\mathrm{Ce}{\mathrm{O}}_2$ and ${\mathrm{Ce}}_2{\mathrm{O}}_3$. For $\mathrm{Ce}{\mathrm{O}}_2$, the $\mathrm{LDA}+\mathrm{U}$ results are in better agreement with experiment than the $\mathrm{GGA}+\mathrm{U}$ results whereas for the computationally more demanding ${\mathrm{Ce}}_2{\mathrm{O}}_3$ both approaches give comparable accuracy. Furthermore, as expected, ${\mathrm{Ce}}_2{\mathrm{O}}_3$ is much more sensitive to the choice of the U value. Generally, the PW91 functional provides an optimal agreement with experiment at lower U energies than LDA does. In order to achieve a balanced description of both kinds of materials, and also of nonstoichiometric $\mathrm{Ce}{\mathrm{O}}_{2-x}$ phases, an appropriate choice of U is suggested for $\mathrm{LDA}+\mathrm{U}$ and $\mathrm{GGA}+\mathrm{U}$ schemes. Nevertheless, an optimum value appears to be property dependent, especially for ${\mathrm{Ce}}_2{\mathrm{O}}_3$. Optimum U values are found to be, in general, larger than values determined previously in a self-consistent way.