# How do you sum a series when individual elements themselves may be series?

Okay Math SE, I've got a problem to fry your brains over. Let's see who can get this.

Consider this:

A cube exists in the euclidean space, it seemingly has the power to divide itself into a copy. But it can only do so eight times. Any copy of the cube generated also has this ability but its ability is weaker than the original cube. This means that if the original cube has the ability to divide 8 times, a copy of it has the power to divide 7 times. Any copy of a clone cube carries over the same ability weakened with a one less value of multiplicity than the original clone cube. A very important rule is that any cube, no matter clone or original, loses a bit of its power after a single go of division. That is, the original cube after dividing once will have the ability to divide 7 more times again but any clone it produces afterwards will have one less from that number, that is 7-1 = 6 allowed to be created. A cloned copy of the cube the first time can divide 7 times more, any clones of it again can divide 6 times from then on

Math SE, how many cubes are there in total after all the divisions are complete (excluding the original cube)?

PS: Huge hint in the title (use it at your own risk though, may be applicable OR may be misleading) Also if someone can suggest a better title or perhaps edit it in (rather than a "brainteaser yaay"), I would welcome it.

A single 8-cube turns into two 7-cubes, which turn into four 6-cubes, into eight 5-cubes, and so on, giving finally $2^8 = 256$ 0-cubes (i.e. just cubes).