Here goes;
I was a Refrigeration Service Technicain for 15 years. The concept of refridgeration isn't putting cold air into a area, it is infact, just the opposite, removing heat from an area. The Refrigerant in it's low pressure, low temperature vapor state moves through the evaporator-which is located inside of the refrigerator or area such as walk-in cooler or other similar type area, and picks up the heat-removes the heat- from the area. The removal of heat from the area is what gives you the cold temperature. The more heat in the area, the more energy it takes to remove that heat, so there are quite a few variables needed to answer your question correctly, such as, is the beer warm or cold when put into the fridge? What is the outside temperature, how well is the box sealed, ect. If the beer was already cold-the same temperature as the refrigerator is when it is running, it would take the same amount of energy to keep the temperature constant whether the refrigerator was full or empty. Once the desired temperature is reached, if the box is kept closed and sealed, it would take the SAME amount of energy to keep the refrigerator at the desired temperature whether it was full or empty. If you filled the chilled refrigerator with warm beer, it would take more energy to run. Hope that this info helps you out, LMK if you have any other questions.