Calculating Sphere Cube Intersection

Hello, I want to evaluate wether a given sphere intersects a cube/parallelepiped or not. A normal check on the distance from the 6 planes forming the 3-d cube will furnish false positives. My idea is to calculate the unit vector between the center of the cube and the center of the sphere, then the intersection between this direction and the cube, so I can check if this distance is greater than the sphere radius or not. But I do not know how to calculate the intersection between a given direction and a cube/parallelepiped. Thanks.