Generalized cubic partitions

A cubic partition consists of partition pairs $(\lambda ,\mu )$ such that $\mathrm{\mid }\lambda \mathrm{\mid }+\mathrm{\mid }\mu \mathrm{\mid }=n$ where $\mu$ involves only even integers but no restriction is placed on $\lambda$. This paper initiates the notion of generalized cubic partitions and will prove a number of new congruences akin to the classical Ramanujan-type. The tools emphasize three methods of proofs. The paper concludes with a conjecture on the rarity of the aforementioned Ramanujan-type congruences.