The nonlinear optical response of (hetero)adamantane-type clusters and organotetrel molecules with the general formula [(RT)4E6] and [TR4] (T = group 14, R = organic substituents, E = S, CH2) is investigated from first principles. These clusters have been reported to efficiently convert infrared radiation into white light and are therefore extremely attractive functional materials for a multitude of applications. We demonstrate that the optical nonlinearities of the clusters in the range from 0 to 3 eV have their origin in electronic transitions within the substituents. The cluster core does not directly take part to the generation process; however, it strongly affects the intensity of the linear and nonlinear response. The relationships between optical properties and cluster symmetry, stoichiometry, substituent field, core composition, and further structural characteristics are investigated by systematical variation of R and T. This also demonstrates the possibility to finely tune the intensity as well as the frequency dependence of the optical response. Upon formation of cluster dimers, the intensity of the nonlinearities depends on the overall dimer geometry. In the case of heterogeneous dimers, the optical response strongly resembles that of a dominant cluster. Similarly, upon formation of cluster crystals, the compound inherits the optical characteristics of the parent molecules.