Bring 1 cup water and sugar to a boil in a saucepan over medium heat, stirring constantly. Boil 3 minutes. Add cinnamon, allspice, and ginger; reduce heat, and simmer, stirring occasionally, 10 minutes.
Pour mixture through a wire-mesh strainer into a Dutch oven, discarding spices. Add apple cider and juices; bring to a boil. Serve hot.