$\tt{\color{#4B4E53}{୨୧ }\text{ }\color{#4B4E53}{i}\color{#5C5F64}{t}\color{#6E7176}{s}\color{#808388}{Z}\color{#92959A}{u}\color{#A4A7AC}{n}\color{#B6B9BE}{n}}$

$\begin{array}{l} \text{Ta có: } a + b + c = 0 \\ \Rightarrow a + b = -c \\ \Rightarrow b + c = -a \\ \Rightarrow c + a = -b \\ \\ A = (a - b)c^3 + (c - a)b^3 + (b - c)a^3 \\ A = ac^3 - bc^3 + cb^3 - ab^3 + ba^3 - ca^3 \\ A = (a^3b - ab^3) + (b^3c - bc^3) + (c^3a - ca^3) \\ A = ab(a^2 - b^2) + bc(b^2 - c^2) + ca(c^2 - a^2) \\ A = ab(a - b)(a + b) + bc(b - c)(b + c) + ca(c - a)(c + a)  \\ A = -abc(a - b) - abc(b - c) - abc(c - a) \\ A = -abc[(a - b) + (b - c) + (c - a)] \\ A = -abc(a - b + b - c + c - a) \\ A = -abc \cdot 0 \\ A = 0 \end{array}$