As an alternative to hiding the holes, you can highlight them, by filling them with a contrasting material. For some projects just filling the holes as they are results in an interesting result. In the case of your goblet, turning a recess where the holes are, and then filling that would probably be a better choice. This would result in a contrasting circle where the holes used to be. Of course this is only an option if you can still mount it on the lathe.
Options for the fill include:
* Wood filler putty
* Dry wood filler powder mixed with a dye
* epoxy mixed with a dye
* powdered metal solidified with thin CA glue
* specialized filler products such as InLace