Undercut the hole using a chisel and hammer to widen the hole. Avoid creating a tapered edge; instead, create an edge at least 1/8-inch thick where possible, as this base helps the patch to last over the long term, recommends the Ask the Builder website.
Use a wire brush to remove loosened cement. Do not smooth the surface as this will affect the bond between the old and new surfaces. Vacuum away any dust.
Brush on cement adhesive or simply moisten the chiseled area. Apply a pre-mixed concrete patch, or mix your own concrete to use as filler using one part Portland cement to two-and-a-half parts fine sand.
Press the cement into the hole with the point of a metal trowel, then smooth over the patch with the trowel to finish.
Allow the surface of the patch to dry for approximately two hours. Cover the patch with a sheet of plastic. Place a small section of 2-by-4 over the plastic and wedge a longer section of 2-by-4 between the floor and the first board to help hold the plastic flush against the patch. Allow the patch to cure beneath the plastic for five days. Wet the cement daily during curing.
Select a product to use as a filler. Products such as polyurethane resins are available which set in high and low temperature conditions. Mix the filler according to directions.
Use a putty knife to apply the filler to the hole, packing it in to fill the deeper portions of the hole before creating a small mound of product over and around the hole.
Finish the area once the patch starts to harden, then sand away any excess filler once the product dries. Cover the patch for several days to cure it. Use the same procedure you use for curing cement, as noted in step five above, except there is no need to remove the plastic to wet the patch. Paint over the hole to disguise the repair and finish the job.