How to calculate the sum

How to calculate the sum

Is there any easy way to calculate $\sum_{a=0}^m \sum_{b=0}^m \sum_{c=0}^m
\min_2(a,b,c)$ as a function of $m$ ?
$\min_2(a,b,c)$ is the second minimum of $a,b,c$. That is if $a \leq b
\leq c$, $\min_2(a,b,c)=b$. $m$ is a positive integer.
Considering all different cases i.e,
$\sum_{a=0}^m \sum_{b=0}^a \sum_{c=0}^b,\sum_{a=0}^m \sum_{b=0}^a
\sum_{c=b}^a, \sum_{a=0}^m \sum_{b=0}^a \sum_{c=a}^m,\\ \sum_{a=0}^m
\sum_{b=a}^m \sum_{c=0}^a \sum_{a=0}^m \sum_{b=a}^m \sum_{c=a}^b,
\sum_{a=0}^m \sum_{b=a}^m \sum_{c=b}^m $
desired sum can be calculated.
I want easier trick as I need also to calculate
$\sum_{a=0}^m \sum_{b=0}^m \sum_{c=0}^m\sum_{d=0}^m \min_3(a,b,c,d)$ and
$\sum_{a=0}^m \sum_{b=0}^m \sum_{c=0}^m\sum_{d=0}^m \min_2(a,b,c,d)$.