On ncatlab page on formality, it is stated that Deligne--Griffiths--Morgan--Sullivan proved that the real homotopy type of a closed Kaehler manifold is formal. Later, Sullivan "improved" this to $\mathbb{Q}$-formality.

My question is: are there some easy examples of closed topological manifolds whose $\mathbb{R}$-homotopy type is formal, but $\mathbb{Q}$-homotopy type isn't?