Find the dissimilar numbers.

Let's check the common arithmetic property connecting the numbers inside each option pair:
* (A) 16, 25: Both are perfect squares ($16=4^2$ and $25=5^2$).
* (B) 49, 81: Both are perfect squares ($49=7^2$ and $81=9^2$).
* (C) 8, 27: Both are perfect cubes ($8=2^3$ and $27=3^3$). They are not perfect squares.
* (D) 4, 9: Both are perfect squares ($4=2^2$ and $9=3^2$).

Since option (C) consists of perfect cube numbers while all other pairs consist of perfect square numbers, 8, 27 is the dissimilar option.