Can someone who is an an intermediate to advanced lifter get into a decently aggressive cut (6-8lbs a month) while building muscle?
ATTENTION!: I am asking if this muscle gain is doable in areas that are beginner looking and performing too such as biceps, calves and shoulders. Thanks!

Once you get into this cut stage you are actually taking in more protein to minimize muscle loss. Plus you need some place to put the remainding calories so more protein is ideal. To build muscle you need to eat in a surplus so gaining muscle while cutting is not ideal especially out of the newbie stage.

I have to agree with Aaron here. If you're an intermediate lifter.. you've been lifting for probably a year or two at least already, right? It's not likely that you're going to be able to build muscle while cutting, rather just preserve as much as you have. UNLESS you are obese.. in which case it might still be possible to do both.

If you haven't been training those muscles you mention though, it's possible they'll see improvements when given more attention.

But lastly, if you are in an aggressive cut, that means you're going to be in a bigger surplus, losing weight faster, and therefore building muscle is going to be even harder compared to if you were doing a slow cut.