Can I apply to Cambridge for Computer Science with these grades?

They won't care about your football background or being a prefect; they only care about your interested, aptitude, and motivation for the course in question. If you have any extracurricular activities related to CS (or subjects relevant to it, such as maths) then that would be of interest to them, but other "generic" extracurricular activities they don't care about at all (they also indicate this, in as many words, on their webpages).

You technically meet the requirements at a glance, however one of your A*s is in a language A-level for your native language; they don't normally consider such A-levels as part of making an offer, and the course requires A*A*A. If they completely disregard this A-level, then your predicted grades don't meet the requirements. Only being predicted an A instead of an A* in A-level Maths might be some cause of concern for them, particularly as you don't have A-level Further Maths.

The combination of both those things makes it a bit harder to say. Worst case scenario though, it's only one of five UCAS choices, so provided you select an appropriate range of course for your other options then it's unlikely you'll come out of the application process with no offers. If you could pull up either A-level Maths or Physics (ideally maths) to a predicted A* I think it's very much a possibility provided you do well (enough) on the CSAT. Without that, I think it might be a bit of a long shot but if you are able to do very well on the CSAT and have a cogent personal statement relating to the subject area, then you might get an interview.

@Doones might be able to give a better perspective on whether it's likely if you might be interviewed or not given the above.

It is unlikely to get an A* in maths to be honest... I read the entry requirements and they didn´t say that they won´t consider a native language, so for that reason I took it. I guess it is better than having 3 A-level, it is not that easy to get an A* in Spanish although I am Spanish, I can tell. About the football background and being a prefect, Really they don´t care about it? Do they prefer someone that has no social life at all and that only studies? I thought that in life there were more important things than spending all your student life in house studying for exams. At least is what the school says, that being an incredible sport man helps a lot, and that is my case, but well I cannot chose their preferences. About what I have done for computer science, I can say that I have created a phone app and a firewall(if that helps). And in case it helps, my cousin studied in Cambridge and got a patent there, she may be able to write a letter to Cambridge recommending me as a student. Thank you very much

The Cambridge CS course is very mathematical, so if you don't think you'll be able to get an A* in Maths it might not be as fitting to your interests. Do bear in mind they can request the A*s required for the course be in specific subjects when making an offer; so you may get an offer specifying A*A*A with an A* in Maths if you are interviewed and made an offer anyway. Doing more A-levels than required is not considered to advantage students, and they are considered on equal footing as those taking 3 A-levels - except where the fourth is A-level Further Maths for STEM subjects.

Unlike in the US, UK universities in general, and Oxbridge in particular, usually don't care about you being "well rounded". They mainly care about how well you are able to cope with the course in question, as you are applying to a specific degree programme (unlike in the US where you just apply "in general" so they use you being well rounded as an indication you could cope with any course of study you choose there - in the UK you've already made that choice when applying). However universities outside of Oxford and Cambridge do tend to consider such things more, although generally the "top" universities tend to put very little weight on such things.

If you look at their admissions pages, this page makes it clearer: https://www.undergraduate.study.cam.ac.uk/applying/what-are-we-looking-for

As you can see, they are wholly concerned with your general academic ability and preparation, as well as your subject specific preparation and motivation. Everything they mention is academic or academic-related. Bear in mind the interviews themselves are academic and normally consist technical questions and problems (the important thing not in being getting the "right" answer, but in demonstrating your thought process in approaching a problem).

Further, on extracurricular matters, from their FAQs:

"What extra-curricular activities will help my chances of admission?
Our admissions decisions are based on academic criteria (ability and potential) and so we expect to see evidence you your ‘super-curricular’ activities – your wider engagements with the area(s) of academic interest, such as reading and other explorations relevant to the course you’ve applied for.
Your participation (or not) in specific extra-curricular activities that aren’t relevant to the course applied for are not taken into account and don’t affect your chances of being made an offer of a place at Cambridge.
However, when composing your personal statement, you should consider the importance that your other university choices may place on extra-curricular activities."

(emphasis mine)

I can't find any specific reference to the native language A-level issue on their admissions pages either, so this may not (or no longer) be the case. However many other UK universities have such policies (and Cambridge may still take it into consideration, particularly as the literary content isn't relevant to CS anyway).

Bear in mind in all of the above, the admissions decisions are in fact undertaken by the colleges, not the university itself. Individual colleges can set additional requirements to the requirements on the main university webpages (e.g. requiring AS/A-level Further Maths) so you will need to check the pages of the college you are considering applying to (or in general what the requirements are, for an open application). Meeting the requirements (or being on track to meet them) on the main webpages is just the minimum standard required for admission.

I can also say that I am a prefect in my boarding house.

And in case it helps, my cousin studied in Cambridge and got a patent there, she may be able to write a letter to Cambridge recommending me as a student.

Thank you very much for your time. So I see that Cambridge is impossible for me... Not having FM its not good I guess. I just love the fact of being programming the whole day that is what I like. I am not that interested in the maths bit but sadly for universities iit s quite important... It is also bad for me that they don´t consider extracurricular stuff that is what I think I have a lot to give... My dream of going to Cambridge is over I guess... Spain is a good place to study too so I shouldn´t worry that much. Thank you all

oh boy

yes you can apply. no you do not meet the entry requirements

There are plenty of other Computing and CS courses in the UK which focus more on programming and software engineering - just not Cambridge (and likewise, Oxford, Imperial, and Edinburgh are, as far as I'm aware, similarly focused on the more mathematical and theoretical aspects). Keep in mind this isn't an arbitrary requirement or preference by them; it's because those courses are in fact very mathematical and theoretically oriented and not really focused on the practicalities of programming so much.

Somewhere like Southampton (which has a specific Software Engineering course) may be more appropriate to your interests and background. It's also considered extremely well in the UK (normally just shy of those "top" courses) for CS (and engineering generally, as the CS faculty is part of a joint EECS department).

No need to be rude... I don´t think I will apply after seeing all this. I don´t want to go to a university where there is no social life as I can see. There are more important things in life than studying.

Imperial basically require further maths too (eventhough it is not explicitly stated) and the social scene there is worse than at Cambridge. Most students on the Computing course will have the mindset of "studying is the most important thing"