Find the dissimilar number:
$216,343,504,512,729$

Let's analyze the given set of numbers to find the pattern:
* $216=6^3$ (Perfect cube)
* $343=7^3$ (Perfect cube)
* $512=8^3$ (Perfect cube)
* $729=9^3$ (Perfect cube)

On the other hand, $504$ is not a perfect cube of any integer ($8^3=512$). Thus, $504$ is the odd or dissimilar number.