All-electron GW calculations of Si, diamond, and SiC were carried out to obtain the quasiparticle energy spectra, for the first time, including both valence and core levels, corresponding to the ultraviolet and X-ray photoemission spectra (UPS and XPS). We used an all-electron mixed basis approach, in which wave functions are expanded with both plane waves and numerical atomic orbitals. In particular for the core states, our results obtained using the perturbative (non-self-consistent) GW approach are in good agreement with available experimental data. The quasiparticle energies of core levels so obtained are also in good agreement with experiments when we do not take into account the renormalization factor z. Moreover, we refer to the bandwidth of diamond and compare with experiments.