That is a somewhat different arrangement than we usually see.
Don't use cement - use plaster - it's much easier to remove when the the time comes, while being perfectly stable until then.
You might try some threadlocking compound on the bolts as a first approach.
For either foam or plaster fill with this arrangement, you'll want to block off the drain pipe area (and probably the far end of the tub as well) to simplify the future.
Polyurethane Foam is both easy, and tricky - it expands after you apply it, so if you put in what looks like enough, it may become too much. Safest to plug the tub and run it half-full of water for ballast - if using the typical cans of foam, squirt one all around on the floor and wait for it to expand and cure before adding more - that will give you an idea of how much it expands. This is a fairly high off the floor installation, so you'll certainly need more than one can (or you could fill some space with a sheet of rigid insulating foam - styrofoam - and then add spray foam on top.)
For plaster, you just mix it up and stuff it in to fill the gap between the floor and the bottom of the tub. On a new tub install the recommended method is to put a pile of it on the floor and set the tub into it. As above, you could take some of the vast space you have on this install out with a sheet of rigid foam.
Given the height, I'm going to strongly suggest the rigid foam sheet as part of your solution, it will make for a much faster, neater fix.