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