re: Any chemicals or cleaning mix that help to clean dirty cement?

Pre-wet your concrete, 50/50 water to bleach will do the trick on most algae. If you have some stubborn areas, up your percent. Scrubbing will only be needed in the worst areas.

They sell bleach in various concentrations. The 50/50 ratio is for the blue bottle of Clorox. If you buy a higher concentration bleach, dilute accordingly.

Add bleach to water, not the other way around. And don’t wear any clothing you like.

If bleach isn’t getting the stains up, you have oil or rust stains. Muriatic acid for the rust, any detergent for the oils.