Multi-layered golf balls having a core made of a foamed composition, preferably polyurethane foam, are provided. The ball includes a dual-layered core having a foam inner core (center) and surrounding outer core layer. The outer core layer may be made from a non-foamed thermoset material such as polybutadiene rubber. The ball further includes an inner cover, preferably made from an ionomer composition comprising an O/X-type acid copolymer, wherein O is α-olefin, and X is a C3-C8 α,β-ethylenically unsaturated carboxylic acid. The outer cover may be made from a non-foamed thermoset or thermoplastic material such as polyurethane. Preferably, the specific gravity of the inner cover is greater than the specific gravity of the outer core, which is greater than the specific gravity of the inner core. The finished ball has good distance and low-spin properties.