Duel Nationality

You can apply, but you won't necessarily get one.

When was your son born?
Where and when were you born?

Your son is eligible for a British passport if you (or his mother) were born in the UK (or, if you were born outside the UK, one of your parents was in the service of the British Crown at the time of your birth).

Best place to check is on the British Government's own website where they have extensive guidance about applying for passports:

https://www.gov.uk/apply-citizenship-british-parent