Due to a strong light absorption by metals, it is believed that plasmonic nanostructures cannot be used for generating intensive radiation harmonics in the UV spectral range. We present results of investigation of the nonlinear optical interaction of laser radiation with a single gold nanostructure in the geometry of the Split-Hole Resonator (SHR) [1, 2] under the-state-of-the-art experimental realized conditions: (1) the laser pulse duration is ultimately short (two cycles of the laser pulse wave) to maximally reduce the thermal effects on the nanostructure; (2) the laser light intensity is ultimately high and close to the air ionization threshold; (3) the geometry of the nanostructure is optimal ensuring a record-high efficiency of the nonlinear optical interaction; and (4) the SHR nanostructure is formed in a single crystal gold nanofilm that is flat on the atomic level. Several multipole plasmon resonances can simultaneously be excited in the SHR nanostructure. A strong nonlinear optical interaction at the frequencies of these resonances that leads to (i) the second-harmonic generation, (ii) the third harmonic generation (THG), and (iii) the light generation at mixed frequencies. The THG near field amplitude reaches 0.6% of the fundamental frequency field amplitude, which enables the creation of UV radiation sources with a record high intensity. The UV light may find many important applications including biomedical ones (such as cancer therapy).