How do I fill in drill holes in exterior brickwork?

Hi , If all the holes are in the masonry joints buy yourself a jointing chisel which is flat angled chisel, chop out about a 3 inch slot on every hole, clean out and mix up some new mortar and point in ,always looks best in my opinion. You will have to match the existing mortar depending on colour, normal mortar should be local building sand /cement or sharp sand/cement you can do some test mixes.

If the holes are in the bricks...Exterior-grade silicone caulk can be shot into the holes using a silicone gun (dampen the area first). Leave a couple of millimetres to flush up and match the hole to the brick. If you grind up a matching brick to get a small amount of brick dust for each hole (Smash it with a hammer works), you can then mix this dust in portions of 4:1 Dust:Cement with a small amount of water to make a paste. This can be used to flush the hole and there should be very little difference from the original brickwork once dry.

You could also try an old wood saw if the joints are very soft . Or hire a mini angle grinder .

I agree with the answer of how to fill in the mortar joints, but would investigate first because she is saying that they are drilled holes it means that someone has put them there for a reason in the first place e.g. airflow, damp problems.