More Cambridge stats from last year.
There were 17,189 applications, resulting in 3497 acceptances.
97% of those who accepted a place at Cambridge last year got A, A, A or higher (includes A, A, B - the best three A levels counting). Modal best is 3 x A.
Of those applicants that were unsuccessful, 4962 also got A*, A, A or better.
These means that almost exactly half of applicants went on to get A level results below A*, A, A.
So, it is pretty unlikely that you will get in if with just As.
Also, other things being equal, if your child is predicted A*, A, A or better, they would be in the top half of applicants when ranked by results.