GPA: 3.6 Unweighted (I know 
)
UC GPA: 4.06
Rank: 62/720
New SAT (2016): 1550, 800 Math, 750 Reading/Writing
Extremely unlikely.
To add extra info:
9th Grade: Calc AB
10th Grade: Calc BC: 5; AP Bio: 5
11th Grade: Physics C Mechanics: 5; APUSH: 5
12th Grade: Taking AP Lit, AP Spanish: And have A’s in Both so far
Math 2: 800
Physics: 800
?
I am more optimistic about your chances, since you are in-state. Obviously you need some strong back-up schools, and there are several where you probably can get a full tuition to free ride scholarship with that SAT score. Are you NMF?
I am not.
Not sure why there should be much optimism. In 2015, frosh applicants to UCB with UC-weighted-capped GPA 3.80-4.19 had only a 12% admission rate. But UCB College of Engineering majors are generally more popular relative to their capacity, so admission selectivity is higher.
UCs appear to prefer higher GPA lower test score over lower GPA higher test scores. But UCB College of Engineering majors likely need higher GPA and higher test scores.
But that is a very high test score, so unless the weighting for that is negligible, I would think his chances are improved even for his GPA. If not, there are many fine schools with strong engineering departments where he would be likely to receive good merit assistance.
While higher test scores are always better than lower test scores, they do not appear to help as much at UCs compared to many other schools. Applicants to UCs should not assume much compensation for lower GPA just because of higher test scores.
There were threads about applicants getting what were surprise-to-them rejections from UC Davis. The most common stat profile for these surprised applicants was similar to the OP’s: GPA in the 3.80-4.19 range (53% admit rate in 2015 to UCD with this GPA range), very high test scores.