I was asked to write this short explanation, it’s not a piece of art and so it probably shouldn’t be in this part of the forum, but I was asked here.
Never mind about that cube in the last two pictures, they don’t belong there and I just failed to remove them.
Additionally the beveling is not done very exact here, but it really doesn’t have to be to show what I mean.
When beveling a cube, I would usually click on subdivide a few times or, if I’m a bit more motivated to get less polygones follow these few steps.
Adding plane and extruding the sides for nice subsurf beveling
Then doing the same in the 3rd dimension
However, this really is a pain and with the knife tool it is a lot easier to do this after all the modeling is done.
So, for knife beveling, just create the object you desire, here once again a cube. (I already subsurfed it, so don’t wonder about it being a sphere)
Then, press k for the knife menu and click on “Knife (Exact)”.
Draw a line over the faces you want to cut, then click.
All selected edges will be cut where the line crosses them.
Finally rotate your viewport and add the last cuts. The beveling is done, and looks essentially just like the beveling done with extrusion.