Multi-layered golf balls containing a dual-core structure are provided. The core structure includes an inner core (center) made from a foam or metal-containing composition, or it has a hollow shell construction, and the outer core layer is made of a thermoplastic composition. Preferably, the thermoplastic composition comprises: a) ethylene acid copolymer, b) plasticizer, and c) cation source. A fatty acid ester such as ethyl oleate is preferably used as the plasticizer. The core assembly preferably has a positive hardness gradient extending across the entire assembly. The core structure and resulting ball have relatively good resiliency at given compressions.