2002 IMO Shortlist S07

What is the smallest positive integer $t$ such that there exist integers $x_1,x_2,\ldots,x_t$ with $$x^3_1+x^3_2+\,\ldots\,+x^3_t=2002^{2002}\,?$$

存在整数 $x_1,x_2,\ldots,x_t$ 且 $$x^3_1+x^3_2+\,\ldots\,+x^3_t=2002^{2002}\,?$$ 的最小正整数 $t$ 是多少