Motivated by Professor N.N. Ganikhodjaev’s pioneering contributions to the analytic theory of quadratic stochastic processes back in the 1990s, we introduce a novel algebraic structure—the so-called Ganikhodjaev multiplication—defined on the vector space of real cubic matrices. This novel multiplication gives rise to what we refer to as the Ganikhodjaev algebra of real cubic matrices. Several open problems and research directions related to the Ganikhodjaev algebra of real cubic matrices are proposed for future exploration. As a practical application, we discuss Ganikhodjaev’s model for the transmission of human ABO blood groups, which has been proposed and utilized by Professor N.N. Ganikhodjaev back in the 2010s, to forecast the potential distribution of ABO blood types in future populations.