Combine white sugar, brown sugar and water in a large saucepan over medium-high heat. Bring to a boil and boil for 5 minutes. Stir occasionally and do not allow to boil over (reduce heat if needed).
Add instant coffee to sugar syrup while syrup is still hot. Stir to dissolve. Let cool.
Pour liquid into glass storage jug or container. Add vodka and vanilla beans. Let stand in a cool, dark location for 2 weeks before drinking.