  The main result of the paper is the existence of an infinitely many families
of Ramanujan-type congruences for $b_4(n)$ and $b_6(n)$ modulo primes $m \geq
2$ and $m \geq 5$, respectively. We provide new examples of congruences for
$b_4(n)$ and $b_6(n)$. Moreover, we find two infinite explicit infinite
families of congruences for $b_4(n)$ modulo $3$.
