Hammurabi did not live in a castle. He lived in a palace located in the city of Babylon, which was the capital of the Babylonian Empire during his reign. Palaces are grand residences that are typically associated with royalty or high-ranking officials. Castles, on the other hand, are fortified structures designed for defense and protection, and they typically have a more medieval or feudal connotation. Hammurabi lived during the ancient Mesopotamian period, well before the time when castles became prevalent.