I am looking for "green" methods to clean cement.

Use a power washer with a surface washer attachment.

Bleach

Pressure wash w water

Oxygen bleach (not Clorox, that chlorine bleach) is 'green' and so is hydrogen peroxide. My guess is that if you search for 'green cleaner for cement' you'll find something you like. This web site does have oxygen bleach and hydrogen peroxide in their article.

http://www.diynetwork.com/how-to/maintenance-and-repair/cleaning/how-to-clean-a-cement-patio

HTH

pressure washer. My husband did our driveway with plain water. It looked brand new

Vinegar and baking soda, a stiff push broom and a hose.

I mopped the garage floor with awesome and then mopped again with clear water. Looked good and the grease and dirt came up.

Wet it and forget it from Lowes or Home Depot.