Originally called the Communist Party of Cuba (Spanish: Partido Comunista de Cuba), it was formed in the 1925 by a group including Blas Roca, Anibal Escalante, Fabio Grobart, Alfonso Bernal del Riesgo and Julio Antonio Mella, who acted as its leader until his assassination in Mexico in 1929.hilst he finished fourth, the party won five seats in the House elections. They won four in the 1950 mid-term elections. In 1961 the party merged into the Integrated Revolutionary Organizations (ORI), the precursor of the current Communist Party of Cuba.