In this talk, we consider n-dimensional Grushin spaces, where a Riemannian metric degenerates along a line in the space, resulting in a sub-Riemannian structure. We discuss the validity of (sub-)mean value property for (sub-)harmonic functions on hypersurfaces within Grushin spaces of dimension n>2. Our interest is driven by the classical counterpart: mean value formulas for harmonic functions on surfaces in the Euclidean setting are crucial for establishing the Bombieri-De Giorgi-Miranda gradient bound, which, in turn, plays a central role in the classical regularity theory. We conclude by presenting remarks and open questions about the regularity theory of minimal surfaces within this sub-Riemannian framework, which is yet to be established.