The volcanic rock used in the Colosseum’s construction was tuff.
Tuff forms when volcanic ash and other pyroclastic material become compacted and lithified into rock. It was widely available in central Italy, where ancient volcanic activity created extensive deposits. Because tuff is comparatively light and workable, Roman builders used it extensively in walls, foundations, and structural sections of major buildings.
The Colosseum was not made from one material alone. Its principal materials included travertine limestone, tuff, and brick-faced Roman concrete. Travertine provided strong exterior structural elements, while tuff helped reduce weight and could be shaped more easily than harder stone. Concrete and brick completed the building’s complex system of arches, vaults, and walls.
Obsidian is also volcanic, but it is a glassy rock associated with blades and decorative objects rather than the Colosseum’s main construction. Granite and basalt were not the specific volcanic rock identified in this question.