A Cayley surface in affine space \({\mathbb{R}}^ 3\) is, by definition, the graph of a cubic polynomial, say, \(z=xy-y^ 3/3\quad or\quad z=xy-x^ 3/3.\) The purpose of the present paper is to characterize a Cayley surface as a nondegenerate surface in \({\mathbb{R}}^ 3\) whose cubic form in nonzero and parallel relative to the induced connection of the surface.