10. Let $f$ be a function from non-negative real numbers to non-negative real numbers, satisfying
$$
f\left(a^{3}\right)+f\left(b^{3}\right)+f\left(c^{3}\right)=3 f(a) f(b) f(c) \text {, (1) }
$$
and $f(1) \neq 1$, where $a, b, c$ are non-negative real numbers. Then $f(2019)=$ $\qquad$
10.0 .

Let $a=b=c=1$, we get $3 f(1)=3 f^{3}(1), f(1)=0, \pm 1$.
According to the condition $f(1) \geqslant 0, f(1) \neq 1$, we know $f(1)=0$. Substituting $a=b=1, c=\sqrt[3]{2019}$ into equation (1), we get $f(2019)=0$.