A complex molecule made up of multiple proteins which is a part of a major catabolic pathway that degrades intracellular proteins after they have outlived their usefulness. An intracellular protein slated for degradation is first marked by the protein ubiquitin, which attaches itself via covalent bonds to the lysine residues of the intracellular protein in a reaction requiring ATP. The proteasome then hydrolyzes the ubiquitinated protein into many small peptides (which also requires ATP) and releases the ubiquitin. Other protease enzymes then hydrolyze the small peptides into individual amino acid molecules. The pathway occurs both in the nucleus and in the cytoplasm of the cell.