Put on a pair of safety glasses and a dust mask.
Use a stiff wire brush to clean out the hole. Brush the inside edges of the hole, as well as the immediate area around the hole on the surface of the block. Remove any paint or other finish that may have been applied to the block. Round off any jagged edges inside the hole.
Wipe the dust away with a clean rag. Use a vacuum to remove any dust you might have missed with the rag.
Dampen a rag with water. Dab the inside edges of the hole with the rag, then dampen the outer surface of the block just around the hole.
Apply a thin coat of concrete bonder to the inside edges of the hole, as well as the outer surface of the block immediately around the hole. Allow the concrete bonder to dry for several minutes until it becomes slightly sticky or tacky.
Insert a piece of 1/2-inch-wide hardware cloth into the hole. Make sure the cloth is down far enough in the hole that it does not extend past the surface of the block. This will give the patching material something to hold on to and support it.
Apply a layer of patching cement to the hole. Use a putty knife or a masonry trowel to spread the patching cement evenly across the hole. Try to apply the cement to the center of the hole first, then slowly add more cement as you work toward the outside edges of the hole. Fill the hole with patching cement until it is flush with the surface of the block. Allow to dry.
Wait at least two weeks before attempting to repaint the block.