How do I stick an object to another without stopping it's movement (not like glue)

One attempt would be to add a force always to the center of the cube.

 using UnityEngine;
 [RequireComponent(typeof(Rigidbody))]
 public class PlanetGravity : MonoBehaviour {
 
     public Transform gravityCenter;
     public float gravityMultiplier;
 
     private Rigidbody rigidBody;
     void Awake()
     {
         rigidBody = GetComponent<Rigidbody>();
     }
     void FixedUpdate()
     {
         rigidBody.AddForce((gravityCenter.position - transform.position).normalized * gravityMultiplier);
     }
 }

Just add this script to your sphere and drop the cube to the gravityCenter. You can also add a physics material to make it bounce a bit and play around with the gravityMultiplier value.