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It is known that the partition functions of the U(N) x U(N+M) ABJM theorysatisfy a set of bilinear relations, which, written in the grand partitionfunction, was recently found to be the q-Painleve III_3 equation. In this paperwe have suggested a similar bilinear relation holds for the ABJM theory withN=6 preserving mass deformation for an arbitrary complex value of massparameter, to which we have provided several non-trivial checks by using theexact values of the partition functions for various N,k,M and the massparameter. For particular choices of the mass parameters labeled by integers$\nu,a$ as $m_1=m_2=-\pi i(\nu-2a)/\nu$, the bilinear relation corresponds tothe q-deformation of the affine SU($\nu$) Toda equation in $\tau$-form.

SU(N) q-Toda equations from mass deformed ABJM theory