Multi-piece golf balls having a multi-layered solid core and multi-layered cover are provided. In one version, a five-piece ball is formed, wherein the inner cover layer is made of a thermoplastic composition such as a highly neutralized (HNP) composition. The outer cover layer is made of a composition comprising a polyurethane, polyurea, or copolymer or blend thereof. In a second version, a six-piece ball having inner and intermediate cover layers that also can be made of HNP compositions is produced. The five and six-piece balls also include multi-layered core structures with a center made of a thermoset rubber. The finished balls have high resiliency and rebounding properties.