Fermat's Last Theorem states that no three positive integers $a$, $b$, $c$ satisfy the equation $$a^n+b^n=c^n$$ for any integer value of $n$ greater than 2.

For this problem we are only considering the case $n=3$. For certain values of $p$, it is possible to solve the congruence equation: $$a^3+b^3\equiv c^3(\mathrm{mod}p)$$

For a prime $p$, we define $F(p)$ as the number of integer solutions to this equation for $1\le a,b,c<p$.

You are given $F(5)=12$ and $F(7)=0$.

Find the sum of $F(p)$ over all primes $p$ less than $6000000$.