Take a look at your bill. The billing date is when your bill prints out. Usually 10 days after that date is when your billing cycle starts. Let's say your bill date is 1/5/14. Your billing cycle would be 1/15-2/14. Or you can check out your bill and see if there's anything on there that shows a period for services rendered, something like 1/1-1/31 that would be your billing cycle.
Anyway, are you asking if you can get cable for one month, cancel it and get it again? As long as you're not under contract for anything, you can make changes.