How do I create a transparent cube, that is, a box in which all the vertices including those normally hidden, are displayed?

There are tools for creating quadrangles and cubes, but they are all filled

Welcome to InkscapeForum!

I'm guessing that you don't mean completely transparent, but rather, unfilled. After you draw a 3D Box, hold Shift and click the black color chip in the palette (or whatever color you want). That will add a stroke. Then click the X at the far left end of the palette, to remove the fill.

If you really do mean transparent, go to Object menu > Fill and Stroke and move the Opacity slider (at bottom of dialog) all the way to the left (value = 0.0). But note that once you deselect it, it will be tricky to reselect!

If neither of those is quite what you need, please clarify

There is the 3D box tool that can create boxes with two vanishing points for some purpose.
You can use that to draw the basic shape, then ungroup the object and colour every face as you wish.
Every face is drawn by the tool, just the fill is opaque by default.

Another way, for ortographic cubes is in the extension menu, by the 3D polyeder drawing tool.
You can adjust the colours of the faces and there is an option of displaying the faces in the background.
You can then ungroup it as well and add other fills/outlines as well.