Transcription factor involved in osteoblastic differentiation and skeletal morphogenesis. Essential for the maturation of osteoblasts and both intramembranous and endochondral ossification. CBF binds to the core site; 5'- PYGPYGGT-3'; of a number of enhancers and promoters; including murine leukemia virus; polyomavirus enhancer; T-cell receptor enhancers; osteocalcin; osteopontin; bone sialoprotein; alpha 1(I) collagen; LCK; IL-3 and GM-CSF promoters. In osteoblasts; supports transcription activation: synergizes with SPEN/MINT to enhance FGFR2-mediated activation of the osteocalcin FGF-responsive element (OCFRE) (By similarity). Inhibits KAT6B-dependent transcriptional activation. {ECO:0000250; ECO:0000269|PubMed:11965546}.