  For a knot $K$ the cube number is a knot invariant defined to be the smallest
$n$ for which there is a cube diagram of size $n$ for $K$. There is also a
Legendrian version of this invariant called the \emph{Legendrian cube number}.
We will show that the Legendrian cube number distinguishes the Legendrian left
hand torus knots with maximal Thurston-Bennequin number and maximal rotation
number from the Legendrian left hand torus knots with maximal
Thurston-Bennequin number and minimal rotation number.
