A simple solution is to do the rotation as an animation where at the end of the animation the cube has moved the +1 distance.

Alternatively use Transform.rotateArount to rotate around a point on the edge of the cube you're currently rolling over.

If not clear what I mean, let me know, can make an example or so.

EDIT: too much fun to pass, here sample code in C# (sorry not too fond of javascript but shouldn't be too hard to convert if you need), Just create new C# class called RollCube and copy/paste code below over it.

EDIT2: now have rotation done from Coroutine so we can delay after rolling to a side.

using UnityEngine;
using System.Collections;

public class RollCube : MonoBehaviour {

    public float cubeSize = 1f; 
    public float cubeSpeed = 50f;
    public float delay = 2f;

    private float totalRotation = 0f; // determines if we're past the 90 degrees
    private float startHeight = 0f; // for correcting height errors

    // next two vars are for determining the corner
    // to rotate over
    private float fwdWeight = 0.5f;
    private float upWeight = -0.5f; 


    // Use this for initialization
    void Start () {
    	startHeight = transform.position.y;
    	StartCoroutine(CORollCube());
    }

    IEnumerator CORollCube() {
    	while (true) {			
    		// we calc the spinamount but make sure it won't shoot over the 90 degrees
    		float spinAmount = Mathf.Min(Time.deltaTime * cubeSpeed, 90f - totalRotation);

    		// we rotate around one of the edges of the cube (the stationary one of course)
    		transform.RotateAround(transform.position + (fwdWeight * transform.forward + upWeight * transform.up) * cubeSize, Vector3.right, spinAmount);

    		// add to amount of spin in this update the total rotation
    		totalRotation += spinAmount;

    		// check if we have to move to the next edge
    		if (totalRotation >= 90f) {
    			// we move to next corner as pivot point
    			totalRotation -= 90f;
    			float t = fwdWeight;
    			fwdWeight = -upWeight;
    			upWeight = t;

    			// make sure height stays correct
    			Vector3 pos = transform.position;
    			pos.y = startHeight;
    			transform.position = pos;

    			// wait for delay amount of seconds
    			yield return new WaitForSeconds(delay);
    		}
    		else {
    			// ready for this frame
    			yield return 0;
    		}
    	}
    }
}

// Reposting this non-working answer because it was unreadable when posted as a comment to the previous answer

var cubeSize : float = 1; 
var cubeSpeed : float = 80;

private var totalRotation : float = 0; // determines if we're past the 90 degrees
private var startHeight : float = 0; // for correcting height errors

// next two vars are for determining the corner
// to rotate over
private var fwdWeight : float = 0.5;
private var upWeight : float = -0.5; 


// Use this for initialization
function Start () {
    startHeight = transform.position.y;
}

// Update is called once per frame
function Update () {

    DoRoll(2);

}

function DoRoll (delay: float) {
    var spinAmount : float = Time.deltaTime * cubeSpeed;
	var t : float;
	var pos : Vector3;

    // we rotate around one of the edges of the cube (the stationary one of course)
    transform.RotateAround(transform.position + (fwdWeight * transform.forward + upWeight * transform.up) * cubeSize, Vector3.right, spinAmount);

    // add to amount of spin in this update the total rotation
    totalRotation += spinAmount;

    // check if we have to move to the next edge
    if (totalRotation >= 90) {
            // we move to next corner as pivot point
            totalRotation -= 90;
            t = fwdWeight;
            fwdWeight = -upWeight;
            upWeight = t;

            // make sure height stays correct
            pos = transform.position;
            pos.y = startHeight;
            transform.position = pos;
        	print ("At rotation " + totalRotation);
			yield WaitForSeconds(delay);

    }
}