Thermally activated delayed fluorescence (TADF), a unique molecular fluorescence mechanism, plays a key role in designing emitters of high efficiency. Carbon fullerenes such as C₆₀ and C₇₀ exhibit strong TADF with intensity even higher than that of the prompt fluorescence, owing to their long lifetimes of triplet state and modest singlet-triplet energy gaps. Thus, there arises the intriguing question whether other fullerene-like clusters can also have fluorescence and host the TADF effect. In this work, by time-dependent density functional theory (TD-DFT) calculations, we explore the excited-states of the experimentally reported boron nitride cage clusters B₁₂N₁₂, B₂₄N₂₄ and B₃₆N₃₆, as well as compound clusters B₁₂P₁₂, Al₁₂N₁₂ and Ga₁₂N₁₂ with the same geometry as B₁₂N₁₂. Using the HSE06 hybrid functional, the predicted energy gaps of these fullerene-like clusters are obtained to range from 2.83 eV to 6.54 eV. They mainly absorb ultraviolet light, and their fluorescence spectra are all in the visible range from 405.36 nm to 706.93 nm, including red, orange, blue, and violet emission colors. For the boron nitride cages, the energy gap of excited states increases with the cluster size increasing, accompanied by a blue shift of emission wavelength. For the clusters with B₁₂N₁₂ geometry and different elemental compositions, the excited energy gap decreases as the atomic radius increases, resulting in a red shift of emission wavelength. In addition, the highest occupied molecular orbitals (HOMOs) and lowest unoccupied molecular orbitals (LUMOs) of these compound cage clusters are distributed separately on different elements, resulting in small overlap between HOMO and LUMO wavefunctions. Consequently, these fullerene-like clusters exhibit small singlet-triplet energy differences below 0.29 eV, which is beneficial for the intersystem crossing between the excited singlet state and triplet state, and hence promoting the TADF process. Our theoretical results unveil the fluorescence characteristics of cage clusters other than carbon fullerenes, and provide important guidance for precisely modulating their emission colors by controlling the cluster sizes and elemental compositions. These experimentally feasible fullerene-like compound clusters possess many merits as fluorophors such as outstanding stabilities, non-toxicity, large energy gap, visible-light fluorescence, and small singlet-triplet energy gap. Therefore, they are promising luminescent materials for applications in display, sensors, biological detection and labelling, therapy, and medicine.