Elementary proofs of infinite families of congruences for Merca’s cubic partitions

Recently, using modular forms and Smoot’s Mathematica implementation of Radu’s algorithm for proving partition congruences, Merca proved the following two congruences: all \(n\ge 0,\)$$\begin{aligned} A(9n+5)&\equiv 0 \pmod {3}, \\ A(27n+26)&\equiv {3}. \end{aligned}$$Here, A(n) is closely related to function which counts number cubic partitions, partitions wherein even parts are allowed appear in different colors. Indeed, defined as difference between n into an numbers odd parts. In this brief note, we provide elementary proofs these congruences via classical generating manipulations. We then prove infinite families non-nested Ramanujan-like modulo 3 satisfied by Merca’s original serve initial members each family.