The way I do it is by using a single radial gradient and a clipping mask.
Follow the steps:
- Create a rectangle the size of your document and fill it with white or light grey.
- Create a larger rectangle and instead of a color fill, use a gradient with the first bottom gradient slider set to opacity and location 0 and the second bottom gradient slider set to opacity and location 100.
- Double click on the second gradient slider and choose a darker grey.
- Click on the top gradient slider that's in the middle right now and set it to 75 instead of 50.
- Center both rectangles and send the bigger one to back.
- Create a clipping mask (Ctrl+7) and that's all.
From here on it's up to you to play with the shapes and colors.
Good luck !
- Draw a rectangle and set it the color you want the corners to be.
- Grab the Gradient Mesh Tool
- Click once in the center of the rectangle
- Change the color
- You can then move the anchor handles to adjust the effect if you wish.
The gradient is a bit rough in the animation due to the gif format and a desire to keep image size small. But in reality the gradient will be nice and smooth.