In the picture I've selected the edge loop I would like to see "cut out" like a bevel, so like a kind of groove in the cube's surface. The Bevel Modifier only seems to work on edges that are at the cube's actual edges. I tried assigning the loop edge to a vertex group, and then select "vertex group" in the bevel modifier, but to no avail. Please advise
Do 3 loop cuts (Ctrl+R) really close to eachother. Then select the one in the middle (Alt+Right Click) and scale it down (S).
Another option would be to separate the mesh by the selected loop. I don't remember if you can do that, but you can always select half the cube and make it a new object (P), then join it back again (Ctrl+J).
Excuse my poor answer but I don't have Blender on this computer to give you some pictures.
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$\begingroup$ Definitely! I've also done something similar with the Subsurf Modifier, where the solution was to add a loop cut really close to another one. $\endgroup$ – Samuel Rocha García Dec 29 '15 at 19:35
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$\begingroup$ Works! But is there also a way to do it using a Modifier? In that way the geometry doesn't get "destructed". You know, where the edge loops is marked as a "bevel edge" or something, and the cutting out is then done automatically (and reversibly) by the Modifier. $\endgroup$ – TavernSenses Dec 29 '15 at 19:36
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$\begingroup$ I don't really know, but if you go for my first option you would only be adding some extra vertices. The second option will disconnect your mesh in two pieces. Edit: No, sorry. It's just the way it works, it needs to have a difference in height to make a bevel. $\endgroup$ – Samuel Rocha García Dec 29 '15 at 19:42
Using the bevel tool (CtrlB) you can create a couple of loop cuts parallel to the edge you want to indent.
Then select the middle loop ring and scale it down:
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$\begingroup$ Yes, that's what I meant. You only missed to add the bevel modifier to see the groove the OP was talking about. If this is what he wanted, I think your answer is clearer :) $\endgroup$ – Samuel Rocha García Dec 29 '15 at 16:34