Find the dissimilar numbers.

Let's investigate the common mathematical parameters of the pairs in each option:
* (A) 16, 25: Both numbers are perfect squares ($4^2=16$ and $5^2=25$).
* (B) 49, 81: Both numbers are perfect squares ($7^2=49$ and $9^2=81$).
* (C) 8, 27: Both numbers are perfect cubes ($2^3=8$ and $3^3=27$). They are not perfect squares.
* (D) 4, 9: Both numbers are perfect squares ($2^2=4$ and $3^2=9$).

Since option (C) contains perfect cubes while all other options contain perfect squares, 8, 27 is the dissimilar pair.