There is definitely more going on with LLMs than just direct parroting.

However, there is also an upper limit to what an LLM can logic/calculate. Since LLMs basically boil down to a series of linear operations, there is an upper bound on all of them as to how accurately they can calculate anything.

Most chat systems use python behind the scene for any actual math, but if you run a raw LLM you can see the errors grow faster as you look at higher orders of growth (addition, multiplication, powers, etc.).