1 x 1 x 1 = 1
12 x 12 x 12 = 1728
1 + 1728 = 1729
9 x 9 x 9 = 729
10 x 10 x 10 = 1000
729 + 1000 = 1729
Therefore, 1 cubed plus 12 cubed = 1729 and 9 cubed plus 10 cubed also equals 1729. Thus, no error in the statement.
In fact, a shorter answer is that:
(one cubed plus two cubed) cubed plus three cubed = 1729,
which fact was posted a few days ago, also.
Got that?