If you control no legendary creatures or legendary planeswalkers, you can activate Mox Amber's ability, but you won't add any mana.

Mox Amber's ability adds one mana of the color of your choice from among the colors of legendary creatures and legendary planeswalkers you control. It doesn't add one mana of each of those colors.

If your legendary creatures and legendary planeswalkers are all colorless, you can activate Mox Amber's ability, but you won't add any mana. Colorless is not a color.