As long as you're going to create 8 different listeners, differentiate them with the JButton.
Button_Square.addMouseListener(new DrawingCanvas(Button_Square));
Button_Square.addMouseMotionListener(new DrawingCanvas(Button_Square));
Button_Rectangle.addMouseListener(new DrawingCanvas(Button_Rectangle));
Button_Rectangle.addMouseMotionListener(new DrawingCanvas(Button_Rectangle));
Button_Circle.addMouseListener(new DrawingCanvas(Button_Circle));
Button_Circle.addMouseMotionListener(new DrawingCanvas(Button_Circle));
Button_Triangle.addMouseListener(new DrawingCanvas(Button_Triangle));
Button_Triangle.addMouseMotionListener(new DrawingCanvas(Button_Triangle));