On 3 and 9-regular cubic partitions

Let $a_3(n)$ and $a_9(n)$ are 3 and 9-regular cubic partitions of $n$. In this paper, we find the infinite family of congruences modulo powers of 3 for $a_3(n)$ and $a_9(n)$ such as $$a_3(3^{2\alpha }n+\frac{3^{2\alpha }-1}{4})\equiv 0(\mathrm{m}\mathrm{o}\mathrm{d}{3}^{\alpha })$$ and $$a_9(3^{\alpha +1}n+3^{\alpha +1}-1)\equiv 0(\mathrm{m}\mathrm{o}\mathrm{d}{3}^{\alpha +1})\mathrm{.}$$