The ¹⁶O nucleus is treated as a bound state of the four-alpha-particle system showing 3α + α clustering. The pair interaction of the alpha particles involved is simulated by a phenomenological potential. Additional three-particle potentials are introduced in order that the entire system and its three-particle subsystems be bound. The parameters of these potentials are determined by fitting the experimental values of the binding energies and the root-mean-square radii of the ¹²C and ¹⁶O nuclei. The calculations are performed on the basis of the s-wave differential equations for the Faddeev and Yakubovsky components. The ground and the first excited state of the ¹⁶O nucleus are investigated. The most probable spatial arrangement of the alpha-particle clusters in the system is determined. The charge form factors are calculated for the ¹²C and ¹⁶O nuclei. The results of our model calculations comply well with experimental data.