  We elucidate the dependence of the Casimir energy on the trace anomaly
coefficients for a six-dimensional CFT on $R\times S^5$. This extends the
universal dependence on the central charge in 2D and the relation by Cappelli
and Coste in 4D, unveiling the role of the trivial total derivatives in the
anomaly that renders the Casimir energy scheme dependent. We obtain
  $$E_o=-\frac{15}{8}\,a_6
-\frac{5}{12}\,\left(g_5+\frac{1}{4}\,g_7+\frac{1}{2}\,g_8-10\,
g_9+g_{10}\right),$$ with $a_6$ being the type A central charge and the $g$'s,
the coefficients of five out of six terms that form a basis for trivial total
derivatives. The derivation is based on the Polyakov formulas (conformal
primitive) resulting from the integration of the trace anomaly.
  Alternatively, on a 6D conformally flat background the above basis is
redundant and one can simplify further to get, in terms of the Schouten scalar
$J$ and the Schouten tensor $V$, Branson's basis for trivial total derivatives
$\nabla^2\nabla^2 J$, $\nabla^2J^2$ and
$\nabla^2|V|^2+2\nabla\cdot(V\cdot\nabla\,J)$ with coefficients $\gamma_1,
\gamma_2$ and $\gamma_3$, respectively, \begin{equation} \nonumber
  E_o=-\frac{15}{8}a_6-\frac{1}{24}\left(\gamma_1-\gamma_2
-\frac{1}{8}\gamma_3\right)~. \end{equation}
