Pre wet the floor/grout and then use Aqua Mix Heavy Duty Tile & Grout Cleaner or Aqua Seal Xtreme. Allow them to dwell then scrub with either rotary scrubber or SYR TIC System Grout Brush. Vac up dirty solution then rinse and repeat. Hey Presto!
Then seal the grout to make it a lot easier on youself.
Kev Martin
Marble Life