  We investigate some Diophantine approximation constants related to the
simultaneous approximation of $(\zeta,\zeta^{2},\ldots,\zeta^{k})$ for
Liouville numbers $\zeta$. For a certain class of Liouville numbers including
the famous representative $\sum_{n\geq 1} 10^{-n!}$ and numbers in the Cantor
set, we explicitly determine all approximation constants simultaneously for all
$k\geq 1$.
