I work in the film business and we build cubes around almost everything for portability. Sounds like you have the perfect table for this project.
You didn't list the height of the cube so, lets call those legs. I would start with the 3' x 4' T&B. Cut and cope both sets of parts and place the bottom rectangle on the table roughly centered. Tack 1 long side to the table to hold it in place (clamps will be in the way). Be sure to tack the outside edges so you can cut the finished product free. Get frame close to square and loosely tack it together but, keep the tacks near the bottom edge. Measure both diagonals and shift the other long side to get the frame square and clamp down.
Stoop down and sight across the long sides to make sure they're in the same plane, shim as needed. This will/can compensate for a table that's not flat (Google Winding Sticks). Once flat and square, tack the other side to the table and weld it out skipping around to minimize distortion.
Clamp or tack the top frame aligned to the bottom frame with the parts oriented like they will live. With angle iron that will be leg down. Weld it out in place and let it cool, which will give you T&B frames that line up perfectly. I usually weld a reference dot on each frame on one corner to keep them oriented. Pull the top frame off and set aside but leave the bottom tacked down.
When I'm building more than one cube, I use the lower frame as a fixture and weld out all of those frames for consistency (always marking the same corner).
Now stand the legs in place but, lean them in slightly and put a healthy tack on the outside corner. This will allow you to adjust the frame to square it up. Have someone help set the top on the legs with the reference marks aligned (leaving a slight gap) and put a healthy tack on the outside corner.
Using a tape measure, square each side and brace diagonally. I tack turnbuckles in the corners so that I can adjust as I go. If you don't have any use scrap steel.
Once everything measures square, walk around several times and eyeball the sides to verify everything planes out. When you weld it out, always place welds in pairs that will contract with opposite forces to minimize distortion.
I know this has been long winded but it's difficult to describe. Squares, magnets and fancy fixtures are often overrated. A tape measure and a good eye is all you need to build a cube that doesn't rock and roll all over the floor. Best of luck