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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 aLegendrian version of this invariant called the \emph{Legendrian cube number}.We will show that the Legendrian cube number distinguishes the Legendrian lefthand torus knots with maximal Thurston-Bennequin number and maximal rotationnumber from the Legendrian left hand torus knots with maximalThurston-Bennequin number and minimal rotation number.

An infinite family of Legendrian torus knots distinguished by cube number