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Grease an oval souffle dish with the butter. In a saucepan, bring the garlic and cream to a simmer. Season with salt and white pepper. Simmer the cream for 15 minutes, or until the cream has reduced by 1/4 and has slightly thickened. Season the potatoes with salt and white pepper. Alternate layering the white potatoes, sweet potatoes, red potatoes, and cheese in the prepared dish. You should have a total of six layers. Strain the garlic from the cream and pour over the potatoes. Cover the souffle dish with aluminum foil. Place in the oven and bake for 30 to 35 minutes. Remove the foil and continue cooking for 10 minutes or until the top is golden brown. Cool the gratin for 10 minutes before serving. Garnish with 2 tablespoons each of cheese and chopped chives.