In a large pot, combine the potatoes, sugar, cinnamon stick, and whole cloves. Add enough water to just barely cover the potatoes. Partially cover the pot and simmer, over low heat, until the potatoes are tender, about 20 minutes. Drain and add the potatoes to a large bowl. Discard the cinnamon stick and the whole cloves.
Melt the butter in a medium skillet over medium-high heat. Stir in the ground cinnamon, cayenne, salt, and ground cloves. Pour the mixture over the potatoes and mash to the desired consistency. Transfer to a serving bowl and serve hot.