  We obtain a uniform decomposition into Casimir eigenspaces (most of which are
irreducible) of the fourth power of the adjoint representation
$\mathfrak{g}^{\otimes 4}$ for all simple Lie algebras. We present universal,
in Vogel's sense, formulae for the dimensions and split Casimir operator's
eigenvalues of all terms in this decomposition. We assume that a similar
uniform decomposition into Casimir eigenspaces with universal dimension
formulae exists for an arbitrary power of the adjoint representations.
