Preheat an outdoor grill for medium heat, and lightly oil the grate.
Heat the garlic and butter in a small saucepan over low heat for 5 minutes to infuse the butter with the flavor of garlic. Do not let the butter simmer. Stir together the sugar, salt, black pepper, and cumin in a small dish. Stir into the butter mixture along with the lime juice and hot sauce until evenly blended. Brush the ears of corn generously with the garlic butter; reserve remaining butter.
Cook the corn on the preheated grill, rotating occasionally until the corn is hot and tender, 10 to 15 minutes. Brush the corn with the remaining butter as the corn cooks.
Aluminum foil can be used to keep food moist, cook it evenly, and make clean-up easier.