So the rules for good subdivision topology, which you're violating and which are responsible for your artifacts, are:
Quads only-- no ngons, and minimal triangles.
No 6+ poles.
Put 3 and 5 poles on the most planar parts of your mesh-- definitely not at places where your mesh has a right angle.
There are other rules. The rules only really matter for non-...
Going around the cube this way:
You have a continuous face loop, regardless of its ngon status, because the connecting faces just have one edge between them.
If we "unwrapped" the shape in the direction you're cutting it would look like this (I've only shown three sides)
If we went the other direction it would look something like this, with a ...
Using same code from Add Cuboid.
Test Run, first linked mesh in question, bisecting (2, 2, 2) 3x be same as running once with (8, 8, 8)
Another take on this is to use the same method as outlined in https://blender.stackexchange.com/a/102239/15543
Since all the edges are aligned in X, Y and Z can select on each and cut.
Note this is not joining the meshes, ...
In regards to your cylinder: creating holes or extrusions on curved surfaces are no doubt tricky. One standard way of controlling subdivision modifier are holding edges:
This will change the shape of the cylinder also where you don't want it to be changed:
The change will be the smallest if after pressing CTRL + R, and clicking, you right-click to let the ...
Usually hard surface modeling workflow avoids to make holes in a sphere exactly due to those problems. Also you should never add subdivision before a bevel. Bevel only works well when the vertices of the sphere are not caught inside the bevel.
When they get to close you see artifacts.
The denser the topology the harder it is to keep vertices away.