Place apple cider, apple juice, sugar, and cinnamon sticks into a large pot. Bring to a boil over medium-high heat, stirring until sugar has dissolved. Remove from heat and discard cinnamon sticks. Allow mixture to cool to room temperature, then stir in grain alcohol.
Pour into sterilized quart-sized canning jars; seal with clean lids and rings and refrigerate until ready to serve. Store in the refrigerator for up to six months.