How to draw a cube with a coordinate system in Swing

Question

I have a cube and there is a need to add a 3D coordinate system to it.

There is an example my coordinate system with a cube should approximtely look like:

Unfortunately, my progress seems so far from this example:

Maybe, I can find out how to draw X and Y axis, but I have no idea how to add the Z axis. So, how to build the right coordinate sytem?

My code:

import java.awt.*;
import static java.lang.Math.*;
import javax.swing.*;

public class Cube extends JPanel {
    double[][] nodes = {{-1, -1, -1}, {-1, -1, 1}, {-1, 1, -1}, {-1, 1, 1},
            {1, -1, -1}, {1, -1, 1}, {1, 1, -1}, {1, 1, 1}};

    int[][] edges = {{0, 1}, {1, 3}, {3, 2}, {2, 0}, {4, 5}, {5, 7}, {7, 6},
            {6, 4}, {0, 4}, {1, 5}, {2, 6}, {3, 7}};

    public Cube() {
        setPreferredSize(new Dimension(640, 640));
        setBackground(Color.white);

        scale(50);
        rotateCube(Math.toRadians(60), Math.toRadians(10), Math.toRadians(0));
    }

    final void scale(double s) {
        for (double[] node : nodes) {
            node[0] *= s;
            node[1] *= s;
            node[2] *= s;
        }
    }

    final void rotateCube(double angleX, double angleY, double angleZ) {
        double sinX = sin(angleX);
        double cosX = cos(angleX);

        double sinY = sin(angleY);
        double cosY = cos(angleY);

        double sinZ = sin(angleZ);
        double cosZ = cos(angleZ);

        for (double[] node : nodes) {
            double x = node[0];
            double y = node[1];
            double z = node[2];

            node[0] = x * cosX - z * sinX;
            node[2] = z * cosX + x * sinX;

            z = node[2];

            node[1] = y * cosY - z * sinY;
            node[2] = y * sinY + z * cosY;

            x = node[0];
            y = node[1];

            node[0] = x * cosZ + y * sinZ;
            node[1] = y * cosZ - x * sinZ;
        }
    }

    void drawCube(Graphics2D g) {
        g.translate(getWidth() / 2, getHeight() / 2);

        g.setColor(Color.BLACK);
        for (int[] edge : edges) {
            double[] xy1 = nodes[edge[0]];
            double[] xy2 = nodes[edge[1]];
            g.drawLine((int) round(xy1[0]), (int) round(xy1[1]),
                    (int) round(xy2[0]), (int) round(xy2[1]));
        }

        for (double[] node : nodes)
            g.fillOval((int) round(node[0]) - 4, (int) round(node[1]) - 4, 8, 8);
    }

    void drawAxis(Graphics2D g) {
        int x_c = getWidth() / 2;
        int y_c = getHeight() / 2;

        // X - axis
        g.setColor(Color.green);
        g.drawLine(round(x_c + 300), round(y_c), round(x_c), round(y_c));

        // Y- axis
        g.setColor(Color.blue);
        g.drawLine(round(x_c), round(y_c), round(x_c), round(y_c) + 300);
    }

    @Override
    public void paintComponent(Graphics gg) {
        super.paintComponent(gg);
        Graphics2D g = (Graphics2D) gg;
        g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
                RenderingHints.VALUE_ANTIALIAS_ON);

        drawAxis(g);
        drawCube(g);
    }

    public static void main(String[] args) {
        SwingUtilities.invokeLater(() -> {
            JFrame f = new JFrame();
            f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
            f.setTitle("Rotating Cube");
            f.setResizable(false);
            f.add(new Cube(), BorderLayout.CENTER);
            f.pack();
            f.setLocationRelativeTo(null);
            f.setVisible(true);
        });
    }
}