  The cubic partitions of a natural number $n$, introduced by Chan and Kim,
have generating function $\sum_{n=0}^{\infty}a(n)q^n= \frac{1}{(q;
q)_{\infty}(q^2; q^2)_{\infty}}.$ In this paper, we generalize some results of
Chen-Lin, which suggest that $a(n)$ should have analogous properties of the
ordinary partition function. Specifically, we show that for every non-negative
integer $n$, $a(5^4n+547)\equiv 0\pmod{5^2}, a(7^3n+190)\equiv 0\pmod{7^2},
a(7^3n+288 \equiv 0\pmod{7^2} and a(7^3n+337)\equiv 0\pmod{7^2}.$
