i

$z_1^3+z_2^3+z_3^3=z^3$

$x_1^3+x_2^3+x_3^3=1$

1

$1^3+6^3+8^3=9^3$

${\left(1/9\right)}^3+{\left(6/9\right)}^3+{\left(8/9\right)}^3=1$

2

$3^3+4^3+5^3=6^3$

${\left(3/6\right)}^3+{\left(4/6\right)}^3+{\left(5/6\right)}^3=1$

3

$2^3+{17}^3+{40}^3={41}^3$

${\left(2/41\right)}^3+{\left(17/41\right)}^3+{\left(40/41\right)}^3=1$

4

$3^3+{10}^3+{18}^3={19}^3$

${\left(3/19\right)}^3+{\left(10/19\right)}^3+{\left(18/19\right)}^3=1$

5

$3^3+{36}^3+{37}^3={46}^3$

${\left(3/46\right)}^3+{\left(36/46\right)}^3+{\left(37/46\right)}^3=1$

6

$4^3+{17}^3+{22}^3={25}^3$

${\left(4/25\right)}^3+{\left(17/25\right)}^3+{\left(22/25\right)}^3=1$

7

$6^3+{32}^3+{33}^3={41}^3$

${\left(6/41\right)}^3+{\left(32/41\right)}^3+{\left(33/41\right)}^3=1$

8

$7^3+{14}^3+{17}^3={20}^3$

${\left(7/20\right)}^3+{\left(14/20\right)}^3+{\left(17/20\right)}^3=1$

9

$7^3+{54}^3+{57}^3={70}^3$

${\left(7/70\right)}^3+{\left(54/70\right)}^3+{\left(57/70\right)}^3=1$

10

${11}^3+{15}^3+{27}^3={29}^3$

${\left(11/29\right)}^3+{\left(15/29\right)}^3+{\left(27/29\right)}^3=1$