Another really simple one: Calculate the distance between the centers of the two spheres. If this distance is less than the sum of the radius of both spheres, the spheres are intersecting.
We'll name the first sphere 'first' and the second sphere 'second' in absence of any features that better define them:
/// <summary>Test whether two spheres intersect with each other</summary>
/// <param name="firstSphere">First sphere to test</param>
/// <param name="secondSphere">Second sphere to test</param>
/// <returns>True if the spheres intersect each other</returns>
public static bool StaticTest(
Vector3 firstCenter, double firstRadius,
Vector3 secondCenter, double secondRadius
) {
double distance = (firstCenter - secondCenter).SquaredLength;
double radii = firstRadius + secondRadius;
// The spheres overlap if their combined radius is larger than the distance of
// their centers
return distance < (radii * radii);
}
/// <param name="firstSphere">First sphere to test</param>
/// <param name="secondSphere">Second sphere to test</param>
/// <returns>True if the spheres intersect each other</returns>
public static bool StaticTest(
Vector3 firstCenter, double firstRadius,
Vector3 secondCenter, double secondRadius
) {
double distance = (firstCenter - secondCenter).SquaredLength;
double radii = firstRadius + secondRadius;
// The spheres overlap if their combined radius is larger than the distance of
// their centers
return distance < (radii * radii);
}