I have several sunbelievable sunflower bushes and they are annuals, I want to know how to take cuttings from them
You can't take cuttings from an annual plant. The plant will only live for one year - that's what "annual" means.
At least some of the "sunbelievable" (trade-mark) varieties have been bred to be sterile, so they don't waste the plant's energy on producing seed but keep producing more flowers. So you can't collect seed either.
You just have to buy new plants each year.
One of the suppliers (Thompson and Morgan in the UK) do claim they are propagated "from cuttings" but any questions about how to do it on their blogs go unanswered. Possibly, they use the same micro-propagation techniques that are used for some vegetables (e.g. to produce more than 1000 genetically identical onion plants from one parent bulb) which are not possible for non-professionals to copy.
While you can take cuttings from many annual plants (see this article from Iowa State University for example), the ease with which you can get them to root varies from very easy to extremely hard to impossible. Plant breeders sometimes have a goal that end users will have a product that is close to impossible to root from cuttings and will not release a new product into the market until that goal is achieved. They do this because they have found that simply asking people not to take cuttings does not work; people do it anyway.
While plant protected varieties are often very nice, there are many slightly less attractive alternatives that you can easily propagate without running afoul of any contractual agreement with the plant supplier.