Large metallic nanoparticles with sizes comparable to the wavelength of light are expected to support high-order plasmon modes exhibiting resonances in the visible to near infrared spectral range. However, the radiation behavior of high-order plasmon modes, including scattering spectra and radiation patterns, remains unexplored. Here, we report on the first observation and characterization of the high-order plasmon modes excited in large gold nanospheres by using the surface plasmon polaritons generated on the surface of a thin gold film. The polarization-dependent scattering spectra were measured by inserting a polarization analyzer in the collection channel and the physical origins for the scattering peaks observed in the scattering spectra were clearly identified. More interestingly, the radiations of electric quadrupoles and octapoles were resolved in both frequency and spatial domains. In addition, the angular dependences of the radiation intensity for all plasmon modes were extracted by fitting the polarization-dependent scattering spectra with multiple Lorentz line shapes. A significant enhancement of electric field was found in the gap plasmon modes which was employed to generate hot-electron intraband luminescence. Our findings pave the way of exploiting the high-order plasmon modes of large metallic nanoparticles in the manipulation of light radiation and light-matter interaction.