Applying Cambridge for Mathematics with AP exams, STEP?

I am an international student from Turkey who took the following AP Exams with expected grades of 5 in each of them(scores are gonna be released this July)
Ap Physics C Mechanics
Ap Physics C Electricity and Magnetism
Ap Macroeconomics
Ap Microeconomics
Ap Chemistry (took it last year, so I already got a 5 for this one)
Ap Calculus BC
SAT IIs:
Math:800, Chemistry:800
SAT I:
Math: 800, Reading-Writing: 730

My question is that with these scores, do I have any chance of an offer that does not include STEP III? I have solved three STEP III papers for practice so far but could only get grades 1,2,2 respectively.

Not likely. Afaik, all of the Cambridge colleges require the STEP paper for Math.

I think your question is whether the offer will be for the STEP 1&2 or the STEP 2&3 papers? Calc BC doesn’t cover all the Further Math syllabus, so a STEP 1&2 offer is a possibility. You’d want to apply to colleges which aren’t as strong in math though. Or you might be better off applying to Oxford and taking the MAT, which is easier, and you’d then likely have an unconditional offer if you were successful in the interview.

But what are you doing next year - a gap year? Or is it your senior year? If it’s a gap year then taking STEP at the end of it would be very hard if you’re not doing math in the meantime. If it’s your senior year then why won’t you do more math and be better prepared? You’d want to do multivariate calculus and/or linear algebra but also study any remaining parts of the syllabus separately (e.g. online). The biggest problem with doing STEP as a senior without a planned gap year is that you don’t know the result until mid August. That’s one reason the Oxford application process works better for Americans (and anyone else who would normally get an unconditional offer).

Or are you saying you’ve already taken the STEP 3 as a junior and are worried about the result? You’ll have to disclose it anyway, but allowances might be made if you also got an S in STEP 2. In that case it’s best to talk to your top choice college before applying to see if an unconditional offer is a realistic possibility.

I have not taken any STEP exam so far but my question was whether an offer of STEP I&II is possible. Which colleges has the chance to do that?
Besides, I already learned multivariable calculus and differebtial equations topics in an undergrad course and now making youtube videos on complex analysis. Next year is my senior year and I am taking a discrete mathematics and AP statistics course.

I would look at (and potentially contact) individual colleges. Start with the ones in the bottom half of the Tompkins table (https://thetab.com/uk/cambridge/2016/07/23/last-ever-tompkins-table-79615) and look at their websites (e.g. Robinson http://www.robinson.cam.ac.uk/courses/mathematics). But if you are doing math beyond A level already, a good score (at least a 1) in STEP 3 might still be required. If you can’t get that with another year of preparation, then the undergraduate course would probably be a struggle for you anyway.

In general if you don’t have a strong preference, you might be better off applying to Oxford rather than Cambridge, because any offer there (based on the MAT and interview) would probably be unconditional.