Evaluate the double integral over the given region $\mathrm{R}$. \[ \iint_{R}\left(27 y^{2}-10 x\right) d A \quad R: 0 \leq x \leq 3,0 \leq y \leq 2 \] \[ \iint_{R}\left(27 y^{2}-10 x\right) d A= \]

Step 1 ：The given problem is a double integral over a rectangular region. The limits of integration for x and y are given. We can solve this problem by first integrating the function with respect to x, then integrating the result with respect to y.

Step 2 ：First, we integrate the function \(-10x + 27y^2\) with respect to x, keeping y as a constant. The limits of x are from 0 to 3.

Step 3 ：The result of the first integration is \(81y^2 - 45\).

Step 4 ：Next, we integrate this result with respect to y. The limits of y are from 0 to 2.

Step 5 ：The final result of the double integral over the given region is \(\boxed{126}\).