KöMaL 2012 K358

In a warehouse, there are cubical boxes of the same mass and size stacked in the form of a large rectangular block. A worker is loading the boxes onto a truck. In each step, he transfers to the truck one vertical or horizontal layer of boxes, with a thickness of a single box. (He is able to approach the stack of boxes from any direction.) The mass of the boxes is a whole number of kilograms. The total mass of the boxes loaded in the first step is 60 kg, in the second step it is 84 kg, and in the third step it is 112 kg. What may be the total mass of all the boxes, in kilograms?