  The present paper is in a sense a continuation of \cite{PLS}, it relies on
the notation and some results. The problem tackled in both papers is the nature
of the continued fraction expansion of $\sqrt[3]{2}$: are the partial quotients
bounded or not. Numerical experiments suggest an even stronger result on the
lines of Kuzmin statistics. Here we apply different sets of bases for the
vector space $V$, where the adjunction ring $\ZZ\lbrack \sqrt[3]{2} \rbrack$
lives. And as a result we get a criterion for continued fraction convergents in
terms of the coefficient vector from a lattice.
