Imagine a box that is lined with a material that very effectively reflects EM waves of a certain frequency. I then manage to somehow trap a very sizable amount of radiation with that frequency inside that box. Let's say the relativistic mass of all the photons inside the box is equal to 2kg. Would that box then be 2kg heavier than an empty box? What if the box was in deep space, far away from any massive objects, would it require more force to accelerate it to a certain speed than an empty box?