How to scale and move a cuboid so that it fit's between two points?

Well, the easiest way of doing that would be to parent your 1x1x1 standard cube in a empty GO but locally translated to Vector3(0, 0, 0.5). That way the center of the parent object is centered on one side of the cube. you just have to rotate the parents forward axis (aka z-axis) towards your target and set the parents z-scale to the distance between A and B.

// part of a C# script that should be on the parent object
void SetTarget(Vector3 target)
{
    Vector3 direction = target - transform.position;
    transform.rotation = Quaternion.LookRotation(direction);
    transform.localScale = new Vector3(1,1,direction.magnitude);
}

(ps I wrote that from scratch without error-checking)

Anyway, I'm not a friend of scaling. I would try a procedural mesh approach. But that's up to you ;)

Here would be my attempt at trying this: Create a 1x1x1 unit cuboid object, either hidden or in a prefab. When the second click occurs, take the difference in position, transform the distance to the proper coordinate frame and then set the scale based on that distance. Since you have a unity cube made, the distance and scale should be proportional.

I don't know if I understand what you said, but this code created a object "cube" setting two points for the scale, just set a cube object as a prefab.

 #pragma strict
 
 public var myCube : Transform;
 public var Ancho : float = 3;
 public var Alto : float = 10;
 
 public var inputPosA : Vector3 = Vector3.zero;
 public var inputPosB : Vector3 = Vector3.zero;
 
 var result : Vector3;
 
 //var ray : Ray = Camera.main.ScreenPointToRay (Input.mousePosition);
 
 function Update() 
 {
 
 
 if (Input.GetMouseButtonDown(0)){
 
      inputPosA = Input.mousePosition;
 
  }
 
  if (Input.GetMouseButtonUp(0)){
 
      inputPosB = Input.mousePosition;
 
        DrawALine();
      }
 
 
    
 }
 
 function DrawALine() 
 {
     Vector3 posC = ((inputPosB - inputPosA) * 0.5F ) + inputPosA; 
 float lengthC = (inputPosB - inputPosA).magnitude; //C#
     var sineC : float = ( inputPosB.y - inputPosA.y ) / lengthC; 
     var angleC : float = Mathf.Asin( sineC ) * Mathf.Rad2Deg; 
     if (inputPosB.x < inputPosA.x) {angleC = 0 - angleC;} 
 
     Debug.Log( "inputPosA" + inputPosA + " : inputPosB" + inputPosB + " : posC" + posC + " : lengthC " + lengthC + " : sineC " + sineC + " : angleC " + angleC );
 
     var myLine : Transform = Instantiate( myCube, posC, Quaternion.identity ); 
     myLine.localScale = Vector3(lengthC, Ancho, Alto); 
 
     myLine.rotation = Quaternion.Euler(0, 0, angleC);
 }