Golf balls having a multi-layered solid core and multi-layered cover are provided. The center of the core is made of a thermoset rubber material and preferably has a positive hardness gradient. The intermediate core layer is made of a thermoset or thermoplastic composition. The outer core layer is made of a highly neutralized polymer composition. The inner cover is made of a thermoplastic composition, preferably an ethylene acid copolymer. The thermoplastic ethylene acid copolymer ionomer can have acid groups that are partially or highly neutralized. The outer cover is made of a composition comprising a polyurethane, polyurea, or copolymer or blend thereof. The finished ball has high resiliency and rebounding properties.