To assemble the mandarin boats, hollow out both halves of the mandarins. Flip each half inside out so the bight orange side is on the inside.
To make each cocktail: In each of 4 lowball glasses, stir together 1/4 cup of the apple cider and 1 tablespoon of the Spiced Simple Syrup. Top with a mandarin half, hollow side facing up. Add 1 of the sugar cubes and 1 ounce of the high-proof rum to each mandarin. Light on fire and sprinkle with ground cinnamon to create fireworks. Serve immediately.
Spiced Simple Syrup:
Put the brown sugar, apple cider, ginger, cloves and cinnamon stick in a small saucepot over medium heat. Cook until simmering and the sugar is dissolved, about 3 minutes. Allow the mixture to steep as it cools. Strain the spices out of the syrup and discard.