OK.

I assume that all boxes are filled to the top of 2X6 dressed lumber which is 5.5 inches wide.

First the 8 Ea 2' X 14' boxes
Cubic feet equals 2'X14'X5.5"/12X8=102.67 Cubic Feet
102.67/27=3.8CY

Now the 4'X4' beds.
Cubic feet equals 4'X4'*5.5"/12*5=36.67 Cubic feer
36.67/27=1.36 CY

Total Volume of Soil required = 3.8+1.36= 5.16 CY

Or if you want to call your beds an exact 6" tall it comes to 5.66 cubic yards. When I ordered my soil, I purposely over-ordered by about a half a yard (13.5 square feet) to save some for later, to account for some soil shrinkage, and to top off some other beds I already had. Amazingly enough (well, not really amazing...it was to be expected), after a good hard rain, the soil settled enough so that I only have a couple feet of surplus remaining, and am going to need to go and pick up some more and pay by the cubic ft.!

I cheated and used a soil calculator though, hehe.

Thanks so much, now I am worrying that they will not be tall enough, also we have overhead irrigation but I think it best to either water by hand or install drip hoses.