Multi-piece golf balls containing a multi-layered core structure are provided. The core structure includes a small, heavy inner core (center) having a relatively high specific gravity, an intermediate core layer, and a surrounding outer core layer. The layers of the core structure may have different hardness gradients. In one preferred embodiment, each core layer has a positive hardness gradient. The center of the core comprises a metal material such as copper, steel, brass, tungsten, titanium, aluminum, and alloys thereof. The intermediate core layer is preferably formed from a first thermoset composition such as polybutadiene rubber, and the outer core layer is preferably formed from a second thermoset composition. The resulting ball has high resiliency and good spin control.