**Solution:**

Given:
- $xy = 12$
- $xy = 27$

We need to find the value of $x^3y^3$.

To find the value of $x^3y^3$, we first need to find the values of $x$ and $y$.

**Finding the values of x and y:**

To find the values of $x$ and $y$, we can solve the given equations simultaneously.

1. $xy = 12$

2. $xy = 27$

From equation (1), we have $xy = 12$.

From equation (2), we have $xy = 27$.

Since $xy$ is equal to both 12 and 27, we can equate the two equations:

$12 = 27$

This is not a true statement, which means there is no solution that satisfies both equations simultaneously. Therefore, there are no values for $x$ and $y$ that satisfy both equations.

Thus, we cannot find the value of $x^3y^3$ because we do not have the values of $x$ and $y$.

In conclusion, the value of $x^3y^3$ cannot be determined with the given information.