  In this paper, we compute an explicit matrix factorization of a rank 9 Ulrich
sheaf on a general cubic hypersurface of dimension at most 7, whose existence
was proved by Manivel. Instead of using invariant theory, we use Shamash's
construction with a cone over the spinor variety. We also describe an
algebro-geometric interpretation of our matrix factorization which connects the
spinor tenfold and the Cartan cubic.
