Congruences modulo 27 for cubic partition pairs

Let b(n) denote the number of cubic partition pairs of n. This paper aims to study the congruences for b(n) modulo 27. We first establish three Ramanujan type congruences. Then many infinite families of congruences are presented. Finally, we propose two conjectures on the congruences for b(n) modulo 49,81 and 243.