Is it possible to create sharp / pointing vertex with bevel tool or modifier the way it is shown on the right cube?
I am able only to create the type of bevels as on the left cube - to get the results of the right cube I had to select each edge separately and that is obviously not the most efficient way.
If you want to work with modifiers, and it's only about one cube, then you could solve it completely with Geometry Nodes.
Just add a Geometry Nodes modifier, and use this node group:
This will simply create a cube. This has the size specified in the Modifier Properties.
Additionally there is the value Amount, which like the Bevel Modifier changes the size of the bevel.
Basically, I create a cube here, extrude the faces outward, and scale them to create a beveled edge with a $45°$ angle.
Finally, the cube is simply scaled back to the original size, and you have the desired result. 100% procedural.
(Blender 3.2+)
You can use a combination of modifiers to accomplish a similar result as I demonstrate in this question: Sverchok Decimate and Weld
