If $$a+b+c=3abc$$ and $$a,b,c > 0$$ prove that $$(a+b)(b+c)(c+a)\geq 8$$
I can fairly easily prove that $(a+b)(b+c)(c+a)\geq8abc$, but then I get stuck.....since then I cannot move forward
If I was to prove that $abc\geq1$ this would have been easy but I am stuck, please help me.
Any help is appreciated, thanks.
edit:I am incredibly sorry that I remembered the question incorrectly