证：设x1，x2∈R，且x1＜x2，则：f(x1)−f(x2)＝x13−x23＝(x1−x2)(x12+x22+x1x2)=12(x1−x2)[(x1+x2)2+x12+x22]；∵x1＜x2，∴x1-x2＜0，x1，x2不全为0，(x1+x2)2+x12+x22＞0；∴f（x1）＜f（x2）；∴f（x）=x3是R...