Many moons ago my mother and grandmother lived in a four-plex house which had a stoop with marble steps. Whenever it started to look worn and dingy, Grandma would grab a box of Tide laundry detergent. On her hands and knees, she'd use a stiff scrub brush (not steel) with the Tide granules and would soon have the stoop gleaming white again. If you try this on your marble I wouldn't recommend rinsing it off (for obvious reasons), but instead wipe it off with a broom or a dry cloth.
I'm busy working on my blog posts. Watch this space!