Abstract We have theoretically investigated the electronic states in a core/shell pyramidal quantum dot with GaAs core embedded in AlGaAs matrix. This system has a quite similar recent experimental realization through a cone/shell structure [Phys. Status Solidi-RRL 13, 1800245 (2018)]. The research has been performed within the effective mass approximation taking into account position-dependent effective masses and the presence of external electric and magnetic fields. For the numerical solution of the resulting three-dimensional partial differential equation we have used a finite element method. A detailed study of the conduction band states wave functions and their associated energy levels is presented, with the analysis of the effect of the geometry and the external probes. The calculation of the non-permanent electric polarization via the off-diagonal intraband dipole moment matrix elements allows to consider the related optical response by evaluating the coefficients of light absorption and relative refractive index changes, under different applied magnetic field configurations.