So I want to create a solid object or cube. My big problem is that when I create a cube, the cube is hollow - that is, I can create a cube, subdivide it, and then delete one of the faces, and it is just a hollow, empty cube.
How do I create a cube or fill a cube so that it is full? I want to have layer after internal layer.
Without getting too technical, you cannot create a solid object as you describe in Blender. 3D is already a lie for the most part (basically points and surfaces in virtual space projected to give depth etc). OpenGL, the software interface to graphics hardware that Blender uses draws primitives — points, line segments, polygons etc. and primitives are defined by a group of one or more vertices. In most 3D applications, models are represented as shells or cases where only the surface matter, this makes it easy to edit them for one.
However, there are several ways to fake this in Blender such as using booleans or the bisect tool. These work in a way such that when a part of the mesh is subtracted, the surface(s) of the affected mesh(es) is closed and this gives an illusion of an object being truly solid.
Using booleans (dynamic if you use the modifier)
Using the bisect tool (takes multiple objects into account)
** Images from the Blender wiki.
Blender is the wrong type of software for this. Of course software exists for solid modeling, typically CAD software or simulation software.
With Blender and similar software you define the outside shape of objects (mesh modeling). When it comes to cutting them apart and make them look as if they are filled you would use boolean operators (either directly or as modifier) that simulate filled objects. They calculate new outside faces to make it look as if the inside of the object is filled. Or you would create the geometry and the faces by hand.
So what you want is not possible with Blender. It depends highly on your specific goal if you need to switch the software or if it is better to adapt your process to Blender.
Blender has no concept of a solid volume. Faces are a simplification.
If you are trying to remove the surface of a solid object what do you want to happen? I imagine you want a hole going into the object. This can be done with the extrude operator.
Select the faces you want your hole to be shaped like:
Hit E for Extrude. Move your mouse to change the depth of the effect. Or type in a numeric value with the keyboard. Finish with LMB or Enter.
The extrusion can go both in and out. If your extrusion go out, type in a negative value to make it go in.
Final result can be like:
However, you can use the POV-Ray renderer from within Blender and once it's activated, it's native primitives are available for you to create in the SHIFT+A > POV-Ray menu
