What can cause my 21 day old baby not to poop for three days?

May be normal. Many babies that are breast fed do not have bowel movements sometimes for several days. Breast milk is so perfect it mostly gets absorbed so there is little to poop.
Normal i some. Your typical breast fed baby can have a little poo smear every feeding or one giant blowout every 7-10 days. If soft, i don't consider it constipation. If you formula feed, 3 days is a bit unusual but unless kid poos out thick pellets i wouldn'tworry about it.Wetting every 6 hours or more & feeding vigerously are signs of good basic health.