Actual cubic feet= 288 cf(the entire floor area covered one foot deep), however, realistically you will have to dedicate about 20% of that space to allow access for planting and future harvesting of the mushrooms. That will leave approximately 230 cf of soil capacity (8.5 cubic yards) per level that you can reasonably squeeze in between the floor and the ceiling. I doubt that the floor and roof frame strength will sustain the approximately 1,260 to 1,700 lbs X 8.5 cubic yards that only one layer would weigh depending on the moisture content of the Top Soil used. Somewhere between 10,710 lbs. and 14,450 lbs. per layer. I understand the reason for utilizing the trailer for a mushroom grow house (controlled atmosphere).If you are in a rural area with no neighbors to complain I would recommend that you strengthen the frame substantially and take advantage of the layering effect that is available to your production capacity if the floor support system will withstand the additional weight. It would be much cheaper to bolster the floor than drag in another trailer.
A 7'x16'x18' trailer should be able to hold between 20 and 30 tons of mushroom soil. The exact amount of soil that the trailer can hold depends on its moisture content. These are dimensions of a standard semi dump trailer.