the type of nutrient to give off the most energy is fat.
Fat is one of three Macronutrients (those are nutrients that specifically provide energy, as opposed to other nutrients that provide vitamins and minerals): fat, carbohydrates and protein. It provides 9 calories per gram. Next one is ethanol (alcohol) with 7, but it's not a nutrient( or at least a non-essential one), and then it's carbohydrates and proteins.