This is a golden barrel cactus (Echinocactus grusonii). They can live for at least 75 years, and don't produce flowers until they reach 20 years of age. They can grow to 3 ft (1 m) high and 2 ft wide (0.6 m).
While they are used widely in cultivation, these plants are considered critically endangered in their native home range of Central America. There does not seem to be a lot of information on these plants... In the Huntington library and gardens (where this photo was taken), all of the golden barrels on display had been cultivated from seeds. I don't know if the secondary growths on this cactus are new plants, but I suspect that it is so.