Colloidal systems possess unique features to investigate the governing principles behind liquid-to-solid transitions. The phase diagram and crystallization landscape of colloidal particles can be finely tuned by the range, number, and angular distribution of attractive interactions between the constituent particles. In this work, we present a computational study of colloidal patchy particles with high-symmetry bonding-six patches displaying octahedral symmetry-that can crystallize into distinct competing ordered phases: a cubic simple (CS) lattice, a body-centered cubic phase, and two face-centered cubic solids (orientationally ordered and disordered). We investigate the underlying mechanisms by which these competing crystals emerge from a disordered fluid at different pressures. Strikingly, we identify instances where the structure of the crystalline embryo corresponds to the stable solid, while in others, it corresponds to a metastable crystal whose nucleation is enabled by its lower interfacial free energy with the liquid. Moreover, we find the exceptional phenomenon that, due to a subtle balance between volumetric enthalpy and interfacial free energy, the CS phase nucleates via crystalline cubic nuclei rather than through spherical clusters, as the majority of crystal solids in nature. Finally, by examining growth beyond the nucleation stage, we uncover a series of alternating one-phase and two-phase crystallization mechanisms depending on whether or not the same phase that nucleates keeps growing. Taken together, we show that an octahedral distribution of attractive sites in colloidal particles results in an extremely rich crystallization landscape where subtle differences in pressure crucially determine the crystallizing polymorph.