does a full refrigerator require less energy to cool than an empty one?
Material in a refrigerator acts as ballast. An empty refrigerator requires much less energy to bring from room temperature down to a cool temperature, but it takes more energy to keep at that temperature, because it has no ballast, there is a lot of area for it to leak, to radiate from. A full refrigerator takes a lot of energy to move from room temperature down to its chosen cool temperature at about 38 degrees, but once there, it takes less energy to maintain that temperature, because it has more ballast — when you open the door there is less air to rush out, there is more cool material to help the refrigerator maintain that cool temperature. Think of all that material as storing thermal energy. Once it is stored, that stored energy helps the refrigerator maintain its temperature.