Symmetric sum of $ab(3a+c)$

Question

I'm having difficulty with determining the $\sum_{sym}ab(3a+c)$ involving $3$ variables $a,b,c$. I know the cyclic sum is going to be $ab(3a+c)+bc(3b+a)+ac(3c+b)$, but I'm confused about the symmetric sum. Please include all the terms that are going to get added so I get how we are permuting the variables and how each term would look like. Thanks.