Coat the oily spots with clay-based cat litter. Agitate the clay-based clumps with a broom head to break them up. Leave the cat litter granules to absorb the oil stains for an hour.
Sweep the cat litter into a disposable bag.
Pour liquid dishwashing or laundry detergent liberally onto any remaining oil spots. Detergent emulsifies oily stains.
Douse the soapy oil spots and encompassing concrete with fresh water. Spray the oily concrete with just enough water to generate soapsuds.
Agitate the remaining oil spots with a plastic scrub brush to form a lather. Continue scrubbing the spots until they emulsify and fully disappear.
Blot up the oily soapsuds with paper towels and discard properly.
Rinse the concrete thoroughly with water.