One way to achieve it will be to associate custom userData(URL) with every cube while its being created.
So here is a sample code how we can put data in cubes while they are being generated(in jsfiddle similar logic is used between line 25-63)
var object = new THREE.Mesh(geometry, new THREE.MeshBasicMaterial({
color: Math.random() * 0xffffff }));
object.userData = { URL: "http://stackoverflow.com"};
Now here we use a method called raycasting
to detect mouse click, so in principal when the mouse is clicked, we cast a ray(invisible) in the plane perpendicular to the click and we capture all the objects that the ray intersected.
Then we retrieve the first object from the list of intersected objects because that will be near most the screen
To better understand raycasting and object picking refer to this tutorial.
Now while creating the cubes we already inserted the data so we can simply retrieve(URL) it from the intersected cube and redirect the user to that page.
The sample code will be something like this(at line number 95 in the fiddle )
if (intersects.length > 0) {
window.open(intersects[0].object.userData.URL);
}
Here us a working jsfille hoping it helps