I might be misunderstanding what you would like but I'll give it a shot.
The nut shapes you have aren't solids. You need them to be solids, once you do that, you can boolean difference them from the main object to cut them out. Do this by selecting the outer edges on one side and using "planar". Then switch and do that to the other side. I recommend you temporarily hide the main object to make it easier to work with. Once you have the sides of the nuts created, use boolean union to combine them all together into a single solid. Now that you have the nut solids, you can boolean difference out of the main part.
Be sure to have some margins in what you are creating. If you are designing something for physical construction there are always +/- tolerances to account for.
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