Laplace operators that give $S^d$ eigenvalues that are perfect squares

Question

The Laplace-Beltrami operator on the sphere $S^d$ has eigenvalues $\{ k(k+d-1) : k \geq 0 \}$. Is there a geometrically natural Laplace operator / Laplace like operator (perhaps a Hodge Laplacian or a variant of these Laplacians), defined on a general manifold that instead gives $S^d$ eigenvalues $\{ k^2 : k \geq 0 \}$?