Three numbers in an AP add up to 27, and their product is 504. Find them.

In an AP, $a_n = a + (n - 1)d$ and $S_n = \dfrac{n}{2}\left(2a + (n - 1)d\right) = \dfrac{n}{2}(a + l)$. Choose three numbers as $a - d, a, a + d$, and four as $a - 3d, a - d, a + d, a + 3d$.