The most effective thing I've ever done to re-whiten/clean the grout on my tiled bathroom floor is, sadly, also the most time consuming.
Bleach, gloves, cheap/old toothbrush, scrubbing/brushing w/ the toothbrush, blotting away the dirty liquid w/ a clean paper towel...
If your floor is as cold as mine is,

get ready for a REALLY cold derierre!
In all seriousness though, I have yet to find a product that does it- the only thing I've found is hard labor, no quick fixes...
Upside of this is that the bathroom will be comletely clean after that!