Enlarge the bottom of the cement hole with a metal chisel and hammer. You want the bottom area of the hole to be wider and larger than the top of the hole. This method is called undercutting.
Vacuum loose bits of cement, dirt and dust from the hole with a shop vacuum.
Hang the tip of a garden hose over the edge of the cement hole, and turn the water on. Keep the hole wet and soaked with water for at least one hour. Keeping the hole wet will prevent the cement from soaking moisture out of the patching compound before it has hardened properly.
Allow the standing water to drain out of the cement hole while you create the cement patch by mixing cement mix with water in a large bucket until it resembles a thick paste.
Scoop a grapefruit-sized amount of cement patch mix out of the bucket with a trowel. Force as much cement patch mix into the cement hole as necessary to fill the space. Use the trowel to level and smooth the surface of the cement patch even with the surrounding driveway.
Allow the patched area two hours to set. Cover the area with a sheet of plastic tarp, and then use duct tape to secure all sides of the plastic sheet to the driveway.
Pull one side of the plastic sheet up once per day to mist the area with water. Repeat this procedure for five days to allow the cement patch to cure and harden.