L-system how to make a cube grow

There are many possibilities and you will find many discussions on this forum and on other places.

The main thing is the recursion and the transformation you want.
For a cube, or general case I will say a Brep. Firs part is to choose the face you want to grow.
The face for example could be oriented , scaled and moved toward the sun. The face could also be splitted to have some more branches. You could then loft the faces to make some new brep and apply the recursion on these objects.

But if you want to stay with the cube you’ll have to explain better what you want.

Here an example of a little script I have done to grow circles on a shape.

Here there is bit more constraint as the circles can’t intersect and the attractor is the Z direction.