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In the last decade rare-earth hexaborides have been investigated for their fundamental importance in condensed matter physics, and for their applications in advanced technological fields. Among these compounds, LaB$_6$ has a special place, being a traditional d-band metal without additional f- bands. In this paper we investigate the bulk electronic structure of LaB$_6$ using hard x-ray photoemission spectroscopy, measuring both core-level and angle-resolved valence-band spectra. By comparing La 3d core level spectra to cluster model calculations, we identify well-screened peak residing at a lower binding energy compared to the main poorly-screened peak; the relative intensity between these peaks depends on how strong the hybridization is between La and B atoms. We show that the recoil effect, negligible in the soft x-ray regime, becomes prominent at higher kinetic energies for lighter elements, such as boron, but is still negligible for heavy elements, such as lanthanum. In addition, we report the bulk-like band structure of LaB$_6$ determined by hard x-ray angle-resolved photoemission spectroscopy (HARPES). We interpret HARPES experimental results by the free-electron final-state calculations and by the more precise one-step photoemission theory including matrix element and phonon excitation effects. In addition, we consider the nature and the magnitude of phonon excitations in HARPES experimental data measured at different temperatures and excitation energies. We demonstrate that one step theory of photoemission and HARPES experiments provide, at present, the only approach capable of probing true bulk-like electronic band structure of rare-earth hexaborides and strongly correlated materials.