Multi-layered golf balls having foam center with selective weight distribution

A multi-layered golf ball, comprising:

• a core assembly comprising:
• i) an inner core layer comprising a foamed composition, the inner core layer having a diameter in the range of about 0.100 to about 1.100 inches and a specific gravity (SGinner) and a center hardness (Hinner core center);
• and ii) an outer core layer comprising a non-foamed thermoset or thermoplastic composition, the outer core layer being disposed about the inner core layer and having a thickness in the range of about 0.100 to about 0.750 inches and a specific gravity (SGouter) and an outer surface hardness (Houter surface of OC);
• and
• a multi-layered cover comprising:
• i) an inner cover layer comprising a non-foamed thermoplastic composition having a specific gravity (SGinner cover);
• and ii) an outer cover layer comprising a non-foamed thermoplastic polyurethane composition, wherein the SGinner cover>SGouter core>SGcenter and the Hinner core center is in the range of about 10 to about 60 Shore C and the Houter surface of OC is in the range of about 65 to about 96 Shore C to provide a positive hardness gradient across the core assembly.