I just cleaned white grout in a used house that we just bought. The grout was so dirty you couldn't tell what color it was. I tried Simple Green, Mr Clean, Fantastic, Softsoap, a comercial grout cleaner, and bleach. The product that worked best was TSP from the paint store. I mixed a soultion of 1/2 cup TSP to 1 qt hot water and 1 cup of bleach. That was the directions on the package. I put the soultion on the floor and let it sit for 15 to 20 min, the used a soft scrub brush and a tooth brush (that seemed to work the best). I could believe how clean the grout was after trying all the other things for two days. TSP was also the cheapest.