We report first-principles GW results on the dispersion of the bulk band-gap edges in the three-dimensional topological insulator Sb2Te3. We find that, independently of the reference density-functional-theory band structure and the crystal-lattice parameters used, the one-shot GW corrections enlarge the fundamental band gap, bringing its value in close agreement with experiment. We conclude that the GW corrections cause the displacement of the valence-band maximum (VBM) to the Γ point, ensuring that the surface-state Dirac point lies above the VBM. We extend our study to the analysis of the electron-energy-loss spectrum (EELS) of bulk Sb2Te3. In particular, we perform energy-filtered transmission electron microscopy and reflection EELS measurements. We show that the random-phase approximation with the GW quasiparticle energies and taking into account virtual excitations from the semicore states leads to good agreement with our experimental data.