Multi-layered golf balls having a dual-layered core and cover of at least one layer are provided. The dual-core construction includes a non-foamed inner core (center) made of a thermoplastic or thermoset composition such as polybutadiene rubber. An outer core layer comprising a foamed composition, such as polyurethane foam, is disposed about the inner core. In one version, the foamed outer core layer is made of a relatively soft foam composition having low flex modulus and density. The foamed outer core layer may specific gravity gradient within the layer, wherein the outer surface specific gravity is greater than the midpoint specific gravity. A cover may be disposed about the core structure. For example, an inner cover made of ethylene acid copolymer ionomer and outer cover made of polyurethane may be used.