How to measure the value of density near a center point?

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If I have M points distributed around a center-point, X, in the n-sphere, how to measure the value of density near the center-point, in the selected area?

For example:

In the image1 and image2, I have M points distributed around the center-point (red point). In both images, there are the same number of points. However, in image1, the number of points near the center-point, is higher than the number of points in image2. In this case, how to calculate the density value of image1, which should be higher than the density value of image2.

How to do this with n-sphere.

for example: X = (x1,x2,x3,...xn), where n : dimension