From 1929 to 1961, he taught constitutional law and labour law at the UNAM, where he received several academic honours.
He is mostly noted for his works on labour law, Derecho Mexicano del Trabajo (1938) and El Nuevo Derecho Mexicano del Trabajo (1972), which remain in wide use as textbooks across Latin America.
Infused with the spirit of the Mexican Revolution of 1910, they conceptualized Mexican labour law as having the protection of workers' rights as its chief purpose.
De la Cueva was also a leading advisor in the 1970 revision of the Mexican Labour Code.