Cascaded third-harmonic generation (THG) of femtosecond pulses in a two-dimensional periodically poled lithium niobate is demonstrated experimentally. The poling pattern satisfies quasi-phase-matching conditions for both second-harmonic generation (SHG) and the following sum-frequency generation. The pulse-front tilt in noncollinear interactions compensates for group-velocity mismatch among fundamental, second-harmonic (SH), and third-harmonic (TH) pulses, thereby achieving broad acceptance bandwidths in SHG and THG. A $2\mathrm{mm}$ thick device generates SH and TH pulses of 106 and $110\mathrm{fs}$ , respectively, from fundamental pulses with temporal duration of $118\mathrm{fs}$ and a $1568\mathrm{nm}$ center wavelength. The frequency conversion properties are studied theoretically, and the optimal focusing condition for maximum conversion efficiency is derived.