What makes cola efficient as a rust remover?
Rust consists of insoluble iron oxides and hydroxides, $\ce {Fe2O3·nH2O}$ and $\ce{FeO(OH)·Fe(OH)3}$. Acidifying these compounds protonates the oxide and hydroxide anions to for water:

$$\ce{O^{2-} + 2H^+ \rightarrow H_2O}$$
$$\ce{OH^{-} + H^+ \rightarrow H_2O}$$

This leaves the soluble iron $\ce{Fe(III)}$, which can be washed away.

Many colas contain phosphoric acid, and are quite acidic (Coke has a pH of ~2.5 according to this science fair project), thus they can dissolve the oxides.