@James' answer is brilliant, but further thoughts come to mind.
You are quite possibly playing games which aren't suitable to the entire group.
However, people cheat for different reasons. Sometimes those reasons can be addressed without addressing the cheating.
Games are played for fun
If there's going to be an emotional argument about whether or not the cheating took place, then the 'fun' of game-playing is going to evaporate completely. Far better to enjoy what you can of the game, despite the cheat. If the cheat is fully engaged, the chances are they will stop cheating once they feel they have a chance.
Find games that they don't want to cheat at. There are tens of thousands of games available at any given time..
Although games are (mostly) competitive, gaming is collaborative
It's imperative to choose games that everyone wants to play and that everyone feels they have a good chance of winning at without cheating - this doesn't mean that you believe they have a good chance at winning - they have to believe it themselves, without coercion.
Innocence, Inexperience, Coercion are often factors for cheating. If someone doesn't really want (or doesn't feel able) to play, there's not much point expecting them to follow the rules. If someone doesn't know the rules, or feels unable to meet the current skillset of the other players, they are more prone to cheat.
Likewise, and importantly, cheats tend to be those who need to win, whereas most of us are satisfied by our need to play.
Games like Once Upon A Time and (of course the entire RPG genre such as D&D) have abstracted winning (almost) completely away such that there's nothing to win - there is just the play.
Some games aren't easy to cheat at
Some games, like Monkey Madness, Gulo Gulo, Carcassonne, Coloretto, Kahuna, Taluva, Zendo, (to a degree, Fluxx) are great for playing with cheats because there's nothing to cheat at. (well, with Carcassonne, make sure the cheat isn't operating the scoring track!!)
Many games are collaborative
Play collaborative games with your cheat. There are many fun games available, such as Hanabi, Pandemic, Lord Of The Rings, Unlock, Magic Maze, Mysterium etc. Many of the more recent ones prevent player domination also.