Minimum value of $\,\left(a^3 + b^3 + c^3 -3abc\right)$

Question

If $ a, b , c $ are distinct positive integers satisfying the inequality $ ab + bc + ca \ge 107$. Then what would be the least value of $\left(a^3 + b^3 + c^3 -3abc\right)$ So I basically tried doing two things, first one being applying AM > GM, but I could not because some terms would be negative. The second try was that I simplified $a^3 + b^3 + c^3 -3abc $ into $ \left(a+b+c\right) \left(a^2 + b^2 + c^2 -ab- bc- ca\right)$ but was stuck in finding the minimum values of $ (a+b+c )$. Is there any specific way to solve this problem?