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Partitions wherein the even parts appear in two different colours are knownas cubic partitions. Recently, Merca introduced and studied the function$A(n)$, which is defined as the difference between the number of cubicpartitions of $n$ into an even number of parts and the number of cubicpartitions of $n$ into an odd number of parts. In particular, using Smoot's\textsf{RaduRK} Mathematica package, Merca proved the following congruences byfinding the exact generating functions of the respective functions. For all$n\ge0$, \begin{align*}A(9n+5)\equiv 0\pmod 3,\\ A(27n+26)\equiv 0\pmod 3.\end{align*} By using generating function manipulations and dissections, daSilva and Sellers proved these congruences and two infinite families ofcongruences modulo 3 arising from these congruences. In this paper, byemploying Ramanujan's theta function identities, we present simplified formulasof the generating functions from which proofs of the congruences of Merca aswell as those of da Silva and Sellers follow quite naturally. We also studyanalogous partition functions wherein multiples of $k$ appear in two differentcolours, where $k\in\{3,5,7,23\}$.

Congruences for the difference of even and odd number of parts of the cubic and some analogous partition functions