What happens if you purchase a brand new motorcycle on a credit card and then end up canceling the insurance in the same week as buying it?

If you are speaking of physical damage coverage, if you have no loan or an unsecured loan such as a credit card then you are not required to carry this coverage for the bike itself. However if you plan to drive it over the road, every state has requirements for minimum liability coverages that must be carried. So if you cancel the insurance and still drive it not only are you in violation of the law but if you cause an accident you will be completely liable for any damages and injuries and will have no coverage. Typically minimum limit liability policies are inexpensive.