I am building a 16' deck in Colorado. I will be using 2x8 joists of treated southern pine. Can I candilever 36" past beam?

I would check with the building department that enforces code in your area. I think 3' is way too much, are you 16" on center?

yes, 16" on center using 2x8 treated southern pine

The overhang should not be more than 2 feet, unless you use larger dimension joist and or double up joists, safer to consult an engineer if in doubt. Check with your local building department like ballenger recommends.

Your joists are way too small. You will need 2x10 minimum and more likely 2x12. I think the 3' can't is the most you can go depending on the joist size. I would check your local code, try city hall. Usually they have a deck building guide. If your town doesn't have a deck code get a deck building book. Most have information on joist size and span as well as beam sizing and post spacing.

Well, for some reason I can't find my code book to check the span of an SYP 2x8. A 2x10 on 16" centers will span 15' 3". A 2x8 has to have a span more than 6". Three foot is half of 6 ft. My house has a 2 ft cantilever on 2x10 with two floors and a roof on it. Check with building department but a 3' cantilevered deck with 2x8 on 16" centers should be just fine.