Place cinnamon sticks, allspice and cloves on a double thickness of cheesecloth. Bring up corners of cloth; tie with a string to form a bag.
Place water and spice bag in a large saucepan; bring to a boil. Remove from the heat. Add tea bags; cover and steep for 5 minutes. Discard tea bags and spice bag. Stir in brown sugar until dissolved. Add juices; heat through. Serve warm.