Combine first 3 ingredients in a saucepan, stirring well.
Place cinnamon sticks and remaining 4 ingredients on a 6-inch square of cheesecloth; tie with string.
Add spice bag to cider mixture. Bring to a simmer over medium-high heat, stirring occasionally. Reduce heat to low; cook, uncovered, 15 minutes, stirring occasionally. Remove and discard spice bag. Pour cider mixture into individual mugs. Serve warm.