Sum Of Digits is 43 Puzzle - Solution

The Puzzle:

Sum Of Digits is 43
I am thinking of a 6-digit number. The sum of the digits is 43.

And only two of the following three statements about the number are true:

(1) it's a square number,
(2) it's a cube number, and
(3) the number is under 500000.

Our Solution:

Only Statements 1 and 3 are true. the number is 499849.

7072 = 499849

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