Is there a way to have a negative version of a cube with a grid?

I´m making a proyect where I need to have a 12x12 cube made out of smaller cubes and carve shapes on it by deleting some of the cubes it´s made out of and then next to it make another shape that is the carved shape but the way I´m making it is buy caking pictures of the first one and then by looking at it carvig from scratch the second cube which is very tidious and time consuming, is there a way to get the negative version of my original cube without loosing the grid so I can still edit the individual small cubes?

this is what it currently looks like so you can get an idea of waht i´m trying to do.

This I don’t understand.
But as far as the larger carved shape, it consists of all the smaller cubes that you move over the same distance to the side.
So use an edge somewhere nearby in space as sort of a ruler and move each (selection of) little cube(s) over the distance from endpoint to endpoint of that edge.

p.s. the little cubes are all instances of the same component or at least individual groups

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What I would do if I was starting fresh :
Start with your full cube made of groups
Create 2 Sets of Tags
One called “Positive” and Another called “negative”

Select your entire cube object and make every single group have the same tag, by going to entity info and choosing the positive tag

Now use the search/fetch bar and type “tag” to get to the "tagging tool and select the tag you made called “negative” and click the eyeball next to the negative tag to hide all objects with that tag.

Now use the tag to start tagging the little cubes as the negative space - they will disappear each time you click one as they become tagged and hidden.

You can now toggle the visiblity between positive and negative parts of your sculpt to show either of the 2 versions.

You can even use the color by tag option to make it easier to identify the 2 tags.

This also means you never actually delete anything, so you can easily swap cubes between both states.