Don’t we have a 3 minute mouth swab test for this?
Apparently you may not be able to determine race:
“Another way to look at it: you inherited 50% of your autosomal DNA from each parent, but you didn’t necessarily inherit exactly 25% from each grandparent. Your maternal grandparents contributed exactly 50% in total, but it could be biased in favor of either your maternal grandmother or your maternal grandfather. Same goes for your paternal grandparents.”
If he had a grandparent, say, who was part black, it might not show up.