We have studied the Cu core-level photoemission spectra in the Anderson impurity model for cuprates with different Cu-O networks, dimensionalities (zero, one, two, and three) and Cu valencies (two and three). We focus on the shape of the leading peak and obtain very good agreement with the experimental data. We show how the shape of the spectrum is related to the valence electronic structure and the Cu-O network but also that other atoms can play a role.