Depends on how the whiteboard is meant to be used.

It must be perfectly fine if it's meant to draw figures and overall ideas about the solution. That's what whiteboards are for. Sometimes a picture's worth a thousand words, and drawing diagrams or illustrations is frequently indispensable for actually solving a complex problem (as opposed to having a picture in the head, or described in writing).

But I'd say it's borderline offensive to ask a person to write any realistic code (i.e. not very-high-level pseudocode that's more of a human-readable notes than something for a machine) on a whiteboard.

Never been to Google, so no idea what they ask for.