How about shaking the mixture with water ?

Will it separate the sugar from the oil?

Sugar is much more soluble in water than in vegetable oil, and, as you know, water is immiscible (=not soluble) with oil.

Did you see the result?

The water phase is the bottom layer and

the oil phase is the top layer,

because water is denser than oil.

*You have not shaken the mixture yet, so sugar is still in the oil phase.

Organic Web Chem University of Alberta