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This paper is concerned with the geometry of the Gorenstein locus of theHilbert scheme of $14$ points on $\mathbb{A}^6$. This scheme has twocomponents: the smoothable one and an exceptional one. We prove that the latteris smooth and identify the intersection of components as a vector bundle overthe Iliev-Ranestad divisor in the space of cubic fourfolds. The ninth secantvariety of the triple Veronese reembedding lies inside the Iliev-Ranestaddivisor. We point out that this secant variety is set-theoretically acodimension two complete intersection and discuss the degrees of its equations.

VSPs of cubic fourfolds and the Gorenstein locus of the Hilbert scheme of 14 points on A^6