[citation needed] Cubilla started his career with Paraguayan side Independiente FBC.
In 1986, he signed for Paraguayan side Club Sol de América.
In 1997, he signed for Chinese side Shanghai Shenhua FC.
In 1998, he signed for Brazilian side Foz do Iguaçu Futebol Clube.
[citation needed] Cubilla managed Paraguayan side Club Atlético 3 de Febrero.