How to resize a Summed Area Table/Integral Image? There is very clear explanation on how a Summed Area Table/Integral Image works here: 
https://uk.mathworks.com/help/vision/ref/integralimage.html


How to you scale this SAT/Integral Image? 

For example, I wish to downscale it from 16x16 to 8x8. How would I go about calculating that?
Calculation of the integral image is a linear transform on the original image.

Now, assuming you wanting to downscale the integral image means that you want the result to be the same whether you:


downscale the original image, integrate after
integrate the original image, downscale after


and remember that "downscaling" by a factor of $N$ the original image means


applying a low-pass filter to avoid aliasing and
throwing away $N-1$ of every $N$ pixels.


since low-pass filtering is also a linear operation, we can just switch orders of summations and down-scale the result image. Nothing special applies.