Will upgrading to an RG6 cable improve bandwidth?

If you have rg59 it will likely make a difference. Improving bandwidth though is a hard question. Most times when you use poor quality cable you get lots of errors and drops. Many times it just refuses to work. If you have a very strong signal level from the ISP though it may not make much difference.

You have to look at the numbers in the modem and determine if you are withing acceptable limit for the power and the noise levels. The guide to understanding this is fairly long so I will not repeat it here there are many sites that have quides on how to understand you cable modem numbers.