  We investigate the effect of $k$-cubic spin-orbit interaction on electrical
and thermoelectric transport properties of two-dimensional fermionic systems.
We obtain exact analytical expressions of the inverse relaxation time (IRT) and
the Drude conductivity for long-range Coulomb and short-range delta scattering
potentials. The IRT reveals that the scattering is completely suppressed along
the three directions $\theta^\prime = (2n+1)\pi/3 $ with $ n=1,2,3$. We also
obtain analytical results of the thermopower and thermal conductivity at low
temperature. The thermoelectric transport coefficients obey the Wiedemann-Franz
law, even in the presence of $k$-cubic Rashba spin-orbit coupling (RSOC) at low
temperature. In the presence of quantizing magnetic field, the signature of the
RSOC is revealed through the appearance of the beating pattern in the
Shubnikov-de Haas (SdH) oscillations of thermopower and thermal conductivity in
low magnetic field regime. The empirical formulae for the SdH oscillation
frequencies accurately describe the locations of the beating nodes. The beating
pattern in magnetothermoelectric measurement can be used to extract the
spin-orbit coupling constant.
