Subtract $254.9999999$ from all pixel values, so black corresponds to $-254.9999999$ and white to $0.0000001$.
Find the 2D subrectangle with maximum sum. There are standard $O(n^3)$-time algorithms for this problem (e.g., https://stackoverflow.com/q/19064133/781723, https://www.geeksforgeeks.org/maximum-sum-rectangle-in-a-2d-matrix-dp-27/). As long as you have no more than 10,000,000 pixels in the image, this will be the solution to your problem (since each white pixel contributes another $0.0000001$ to the sum).
Proof that this finds the optimal solution: only all-white subrectangles have a positive sum (if you have a single non-white pixel, then its contributes a negative value of $-0.9999999$ or lower to the sum, which cannot be outweighed by any number of white pixels); and the larger the all-white subrectangle, the larger its sum.