You can use cleaners and elbow grease, but it will be hard to keep it clean.
You may want to consider staining the grout a darker color and save yourself lots of aggravation in the future.
I had the same problem. After much frustration, I stained my kitchen floor grout to a Burgandy Color. (looks great with my rose colored tiles)
That was 12 years ago, and the grout still looks fantasic!
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