there are likely many efficient ways but your initial thought isn’t bad but it’s all going to depend on what you need from your cave, what look you need. if you subdivide your cube (before or after you extrude) you can run a Set Point Value on the points in Crumple mode to roughen the walls or you can use textures and or noises and Displacement to do the same sort of thing (or many different methods combined).
Spherical landscapes can be as easy as the Landscape object with Spherical checked (but that has ‘pinching’ at the poles so might not be what you can use and might not be the right look as well) and you can use the same things mentioned for the cave, Set Point Value and or displacement in textures just to name the simplest methods. What kind of look do you need?