Multi-piece golf balls having a multi-layered solid core and multi-layered cover are provided. In one version, a six-piece ball having a three-layered core and three-layered cover is formed. Preferably, the inner core is made of a thermoset rubber composition, the intermediate core layer is made of a thermoplastic composition, and the outer core layer is made of a highly neutralized polymer (HNP) composition. The cover includes inner, intermediate, and outer cover layers, wherein the outer cover is made of a composition comprising a polyurethane, polyurea, or copolymer or blend thereof. In a second version, a five-piece ball having a two-layered core and three-layered cover is produced. The finished balls have high resiliency and rebounding properties.