Chess.com has very sophisticated cheat detection systems built by chess players and data scientists. GM Hikaru Nakamura was reportedly impressed by their system after being introduced to it by chess.com staff.
The exact inner workings cannot be disclosed for (at least) two very obvious reasons:
- If their algorithm becomes public, players could try to exploit that and evade cheat detection
- The cheat detection system is one of the most important features of a chess platform in the competition against other platforms. chess.com has a very capable system and would help its competitors if they disclosed the exact algorithm.
For these reasons, you cannot expect detailed reasons for their decisions. Neither from any of us nor from them.
They would not ban you at all because you won several games in a row, but they would ban you if your playstyle was indicative of assisted play (i.e. help from an engine / a stronger player) and if their confidence (based on statistical measures) that you cheated is extremely high.
They combine lots of variables (these could be e.g. your rating, quality of your moves, and so on) and calculate the probability for you to have played without assistance, and if that probability for that is very, very low, then they'll ban you after a manual review.
They don't take this lightly and it is very unlikely that you have been banned without reason.
You probably have played moves that were too good for your playing strengths, maybe you played inconsistently (e.g., exceptionally engine-like in difficult situations, but pretty badly without assistance in not-so-critical situations) or too many strong moves that are very difficult to find.
The exact criteria are proprietary, but this should give you an idea.
Please read Chess.com's official explanation here.
Chess.com's fair-play system is thorough, complex and rigorously verified by more than eight years of data from millions of games played by our own members online. Our system gathers and reviews different types of data and other information pulled automatically (and manually) from all member games.
We load these games into a tool that provides the probability that a given player is playing cleanly or with the assistance of a computer engine. Before any accounts are closed, all reports are thoroughly reviewed by a team of specialists who have reviewed and closed thousands of accounts in their roles as Chess.com statisticians.
EDIT: Of course, an absolutely certain proof is impossible to be given (except if they had you and your devices under secret-service-like surveillance), but their evidence is typically so overwhelming, that you would be better off admitting what you did and get a second chance from chess.com.