Permanent seems like a strong word for food coloring... it usually fades with sun and rain over time. Driveways are pretty tough and most spills don't last forever. Have you tried a good scrub or just waiting it out? Blue is a loud color for concrete but it's probably not there to stay... I've seen worse marks come clean with some simple effort.
Permanent dye is actually a real thing for concrete (they sell it at hardware stores). Food coloring might stain less, but some craft dyes are pretty strong. A pressure washer with a concrete cleaner would be the best bet, just waiting might leave a faint mark for years.