Using caulk might seem like the simplest solution. There’s no mixing, and you just have to snip the tip and squeeze the trigger of the caulk gun. Caulks made specifically for patching holes in bricks don’t seem to exist, but you could probably use any caulk labeled as a sealant for exterior use or buy caulk made for patching mortar, such as Quikrete Mortar Repair ($3.48 for a 10-ounce tube at Lowe’s). (The product contains sand, which results in a slightly rough texture, and it’s tinted gray, features that help it blend in with mortar joints.) Because the bricks on your wall have a whitewashed look, which you could only replicate with a light application of paint, make sure whatever caulk you use is paintable. Products that are 100 percent silicone generally are not. For situations where there is no need for paint, tinted silicone caulk, such as the bronze color made for sealing around windows and doors, might be a better option than white caulk.