This paper establishes certain existence and classification results for solutions to SU(n) Toda systems with three singular sources at 0, 1, and∞. First, we determine the necessary conditions for such an SU(n) Toda system to be related to an nth order hypergeometric equation. Then, we construct solutions for SU(n) Toda systems that satisfy the necessary conditions and also the interlacing conditions from Beukers and Heckman [BH89]. Finally, for SU(3) Toda systems satisfying the necessary conditions, we classify, under a natural reality assumption, that all the solutions are related to hypergeometric equations. This proof uses the Pohozaev identity.