The expression of the impact parameter, in the analysis for classical and semiclassical scattering cross sections for black holes, is obtained with nonlinear electrodynamics (NLED) while the absorption section is studied with the sinc approximation in the eikonal limit considering NLED.As an illustration we calculate the classical and semiclassical scattering as well as the absorption sections for three black holes under NLED, the magnetic Bardeen and Bronnikov black holes and the regular Euler-Heisenberg black hole. All are compared with the sections of their linear electromagnetic counterpart, the Reissner-Nordström (RN) black hole. The comparison shows how NLED affects the sections as well as the variation with respect to the Reissner-Nordström sections, in some cases these variations are small.