We explore the effect of a cubic correction gNLϕ3 on the mass function and bias of dark matter haloes extracted from a series of large N-body simulations and compare it to theoretical predictions. Such cubic terms can be motivated in scenarios like the curvaton model, in which a large cubic correction can be produced while simultaneously keeping the quadratic fNLϕ2 correction small. The deviation from the Gaussian halo mass function is in reasonable agreement with the theoretical predictions. The scale-dependent bias correction Δbκ(k,gNL) measured from the auto- and cross-power spectrum of haloes, is similar to the correction in fNL models, but the amplitude is lower than theoretical expectations. Using the compilation of LSS data in [A. Slosar , J. Cosmol. Astropart. Phys.1475-7516 08 (2008) 03110.1088/1475-7516/2008/08/031], we obtain for the first time a limit on gNL of -3.5×105<gNL<+8.2×105 (at 95% CL). This limit will improve with the future LSS data by 1-2 orders of magnitude, which should test many of the scenarios of this type.