Combine apple juice, apple cider, white sugar, brown sugar, and cinnamon sticks in a large pot; bring to almost a boil. Cover pot with a lid, reduce heat, and simmer for about 1 hour. Remove pot from heat and cool completely.
Stir grain alcohol and vodka into syrup and remove cinnamon sticks. Pour apple pie moonshine into clean glass jars or bottles. Store in the refrigerator.
