Good Morning!

It took a while to write that. Why the rum? Long story as a link: I saw that and liked it. Copy, paste, trace out all compile fails and rewrite and present!

The (re-coded) code:

var theScene:MovieClip = new MovieClip();
theScene.x = stage.stageWidth*0.5;
theScene.y = stage.stageHeight*0.5;
addChild( theScene );

var focalLength:Number = 300;

function make3DPoint ( x, y, z)
{
	var point = new Object();
	point.x = x;
	point.y = y;
	point.z = z;
	return point;
};

function make2DPoint (x,y, depth, scaleFactor)
{
	var point = new Object();
	point.x = x;
	point.y = y;
	point.depth = depth;
	point.scaleFactor = scaleFactor;
	return point;
};

function Transform3DPointsTo2DPoints (points, axisRotations)
{
	var TransformedPointsArray = [];
	var sx = Math.sin(axisRotations.x);
	var cx = Math.cos(axisRotations.x);
	var sy = Math.sin(axisRotations.y);
	var cy = Math.cos(axisRotations.y);
	var sz = Math.sin(axisRotations.z);
	var cz = Math.cos(axisRotations.z);
	var x,y,z, xy,xz, yx,yz, zx,zy, scaleFactor;

	var i = points.length;
	while (i--){
		x = points[i].x;
		y = points[i].y;
		z = points[i].z;

		// rotation around x
		xy = cx*y - sx*z;
		xz = sx*y + cx*z;
		// rotation around y
		yz = cy*xz - sy*x;
		yx = sy*xz + cy*x;
		// rotation around z
		zx = cz*yx - sz*xy;
		zy = sz*yx + cz*xy;
		
		scaleFactor = focalLength/(focalLength + yz);
		x = zx*scaleFactor;
		y = zy*scaleFactor;
		z = yz;

		TransformedPointsArray[i] = make2DPoint(x, y, -z, scaleFactor);
	}
	return TransformedPointsArray;
};

var pointsArray:Array = [
	make3DPoint(-50,-50,-50),
	make3DPoint(50,-50,-50),
	make3DPoint(50,-50,50),
	make3DPoint(-50,-50,50),
	make3DPoint(-50,50,-50),
	make3DPoint(50,50,-50),
	make3DPoint(50,50,50),
	make3DPoint(-50,50,50)
];

var ballArray:Array = new Array();

for ( var i:int = 0; i < pointsArray.length; i++){
	var ball:MovieClip = new MovieClip();
	var colors = [ 0xffffff, 0x990000 ];
	var fillType:String = GradientType.RADIAL;
	var alphas:Array = [1, 1];
	var ratios:Array = [0x00, 0xff];
	var matr:Matrix = new Matrix();
	matr.createGradientBox(-40*0.4, -40*0.4, 0, 0, 0);
	var spreadMethod:String = SpreadMethod.PAD;
	var interpolationMethod:String = InterpolationMethod.RGB;
	var focal:Number = -0.1;
	with(ball.graphics)
	{
		beginGradientFill( fillType, colors, alphas, ratios, matr, spreadMethod, interpolationMethod, focal );
		drawCircle(0,0,20);
		endFill();
	}
	theScene.addChild(ball);
	ballArray.push(ball);
}

var cubeAxisRotations = make3DPoint(0,0,0);

theScene.addEventListener( Event.ENTER_FRAME, enterFrameHandler );

function enterFrameHandler( event:Event )
{
	cubeAxisRotations.y -= 5*Math.PI/180;
	cubeAxisRotations.x += 5*Math.PI/180;
	var screenPoints = Transform3DPointsTo2DPoints(pointsArray, cubeAxisRotations);
	for (i=0; i < pointsArray.length; i++){
		var currBall = ballArray[i];
		currBall.x = screenPoints[i].x;
		currBall.y = screenPoints[i].y;
		currBall.xscale = currBall.yscale = 100 * screenPoints[i].scaleRatio;
		//currBall.swapDepths(screenPoints[i].depth);
	}
}

Just don't ask. Yo... -ho!

EDIT: The spam comments, I forgot them. I don't like them. Like: I DON'T LIKE THEM!

EDIT_2: And: Creating the thumbnail was time consuming. More than writing...

EDIT_3: I forgot to include the depths.

function enterFrameHandler( event:Event )
{
	cubeAxisRotations.y -= 2*Math.PI/180;
	cubeAxisRotations.x += 2*Math.PI/180;
	var screenPoints = Transform3DPointsTo2DPoints(pointsArray, cubeAxisRotations);
	screenPoints.sortOn("depth");
	for (i=0; i < screenPoints.length; i++){
		var currBall = ballArray[i];
		currBall.x = screenPoints[i].x;
		currBall.y = screenPoints[i].y;
		currBall.xscale = currBall.yscale = 100 * screenPoints[i].scaleRatio;
		theScene.addChild(currBall);
	}
}