Let's assume the current age of the son is x.
According to the statement, the current age of the man is 6 times the age of the son, so the man's current age is 6x.
20 years later, the son's age will be x + 20, and the man's age will be 6x + 20.
According to the second part of the statement, 20 years later, the man will be twice as old as his son. So, we have the equation:
6x + 20 = 2(x + 20)
6x + 20 = 2x + 40
6x - 2x = 40 - 20
4x = 20
x = 5
Therefore, the current age of the son is 5.
The age of the man when his son was born is given by:
6x - x = 5(6) - 5(1) = 30 - 5 = <<30-5=25>>25 years old. Answer: \boxed{25}.