I have two files:

Squared.java
import javax.swing.*;
import java.awt.Graphics;
import java.awt.event.ActionEvent;
import java.awt.event.KeyListener;
import java.awt.image.BufferedImage;
import java.io.File;
import java.io.IOException;
import java.util.logging.Level;
import java.util.logging.Logger;
import javax.imageio.ImageIO;

public class Squared {
JFrame mainFrame = new JFrame("Squared");
public int x = 5;
public int y = 5;
public boolean canRunConstructor = true;

public static void main (String[] args)
{
Squared mySquared = new Squared();
mySquared.Draw();
}
public Squared()
{
// TODO Constructors
}
public void Draw()
{
canRunConstructor = false;
mainFrame.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
mainFrame.setSize(480,320);
mainFrame.getContentPane().setLayout(null);
KeyEvents keyEvents = new KeyEvents();
mainFrame.addKeyListener(keyEvents);

BufferedImage img = null;
try {
img = ImageIO.read(new File("bin/block.png"));
} catch (IOException e) {
e.printStackTrace();
}
JLabel picLabel = new JLabel(new ImageIcon( img ));
picLabel.setBounds(x,y,40,40);

mainFrame.add(picLabel);

mainFrame.setVisible(true);
}
}

KeyEvents.java
import java.awt.event.KeyEvent;
import java.awt.event.KeyListener;


public class KeyEvents implements KeyListener {

@Override
public void keyPressed(KeyEvent e) {
if (e.getKeyCode() == 39) //Right key
{
Squared mySquared = new Squared();
mySquared.x = mySquared.x + 5;
mySquared.mainFrame.repaint();
}
System.out.println(e.getKeyCode());
}

@Override
public void keyReleased(KeyEvent e) {
// TODO Auto-generated method stub

}

@Override
public void keyTyped(KeyEvent e) {
// TODO Auto-generated method stub

}

}

What i'm trying to do is when I press <RIGHT> in the keyboard, the block moves right, any idea what's wrong? I can't detailedly explain my code now.

My problem there is the Java-talk:

you'll want to have a class which extends JPanel, implements KeyListener, and overrides the method public void paintComponent(Graphics g)

Extending, Implementing and Overriding, but I will give it a look.

That implies changing the Picture Label to a graphic right? Well, I guess i'll have to try that too.

I wrote this to change my code to work with graphics:

Squared.java
import javax.swing.JFrame;
import javax.swing.JPanel;
import java.awt.Color;
import java.awt.Dimension;
import java.awt.Graphics;

public class Squared {
   
    public static void main(String[] args)
    {
        Squared mySquared = new Squared();
        mySquared.createAndShowGUI();
    }

    public void createAndShowGUI()
    {
        JFrame f = new JFrame("Squared");
        f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        f.setSize(480,320);
        f.setResizable(false);
        f.add(new GamePanel());
        KeyEvents myKeyEvents = new KeyEvents();
        f.addKeyListener(myKeyEvents);
        f.setVisible(true);
    }
}

class GamePanel extends JPanel {
int x = 5;
int y = 5;

    public GamePanel()
    {
   
    }

    public Dimension getPreferredSize()
    {
        return new Dimension(250,200);
    }

    public void paintComponent(Graphics g)
    {
        super.paintComponent(g);
        g.setColor(Color.black);
        g.fillRect(x,y,40,40);
    } 
}
KeyEvents.java
import java.awt.event.KeyEvent;
import java.awt.event.KeyListener;

import javax.swing.JPanel;

import java.awt.Graphics;

public class KeyEvents extends JPanel implements KeyListener {
@Override
public void keyPressed(KeyEvent e) {
if (e.getKeyCode() == 39) //Right key
{
GamePanel myGamePanel = new GamePanel();
myGamePanel.x += 5;
//So now how to update graphics?
}
}

@Override
public void keyReleased(KeyEvent e) {
// TODO Auto-generated method stub

}

@Override
public void keyTyped(KeyEvent e) {
// TODO Auto-generated method stub

}
}
My question is how to update the frame after having raised Squared.x to Squared.x+=5. Thanks.

You've already been given the answer.  Don't create a new object each time in that keyPressed event.  Create it once, and use the same gamepanel.

the KeyEvents class shouldn't extend JPanel. That's why the GamePanel class exists. in the Squared class you had a new DrawingPanel, which we'll refer to as "dp1" for simplicity. dp1 is the panel added to the frame, which is seen on your screen. Then you make a new KeyEvents object, which contains a GamePanel. we'll call that dp2. then, whenever you press the right arrow key, dp2's x coordinate is incremented by 5. if the problem in your code isn't apparent by now, refer to the bolded portion of this post.

also, a pro tip. if your class contains instance variables or methods that don't refer to the class name, something's wrong. in this case, your class KeyEvents has a GamePanel object. second, your Squared class doesn't take advantage of constructors. your main method should be as simple as "new Squared();" or "new Squared().show();" -- where show is just frame.setVisible(true); lastly, it's good practice to use constants, e.g. KeyEvent.VK_RIGHT represents the right arrow key, instead of hard-coding it as 39. this makes your code more understandable (eliminating the need for the comment "Right key") and makes it easy to change which number is the right arrow key if needed. for example, you wouldn't write this:
frame.setDefaultCloseOperation(-3);

because -3 has no significant value. if you looked back on that line of code in 3 years you would have no idea what that line does, which is why JFrame.EXIT_ON_CLOSE is used.