John 10:17-18
For this reason the Father loves me, because I lay down my life that I may take it up again. No one takes it from me, but I lay it down of my own accord. I have authority to lay it down and authority to take it up again. This command I received from my Father."
28 Then they led Jesus from Caiaphas to the Praetorium, and it was early morning. But they themselves did not go into the Praetorium, lest they should be defiled, but that they might eat the Passover. 29 Pilate then went out to them and said, “What accusation do you bring against this Man?”
30 They answered and said to him, “If He were not an evildoer, we would not have delivered Him up to you.”
31 Then Pilate said to them, “You take Him and judge Him according to your law.”
Therefore the Jews said to him, “It is not lawful for us to put anyone to death,” 32 that the saying of Jesus might be fulfilled which He spoke, signifying by what death He would die.
33 Then Pilate entered the Praetorium again, called Jesus, and said to Him, “Are You the King of the Jews?”
34 Jesus answered him, “Are you speaking for yourself about this, or did others tell you this concerning Me?”
35 Pilate answered, “Am I a Jew? Your own nation and the chief priests have delivered You to me. What have You done?”
36 Jesus answered, “My kingdom is not of this world. If My kingdom were of this world, My servants would fight, so that I should not be delivered to the Jews; but now My kingdom is not from here.”
37 Pilate therefore said to Him, “Are You a king then?”
Jesus answered, “You say rightly that I am a king. For this cause I was born, and for this cause I have come into the world, that I should bear witness to the truth. Everyone who is of the truth hears My voice.”
38 Pilate said to Him, “What is truth?” And when he had said this, he went out again to the Jews, and said to them, “I find no fault in Him at all.
Thank you! But this particular scene does not take place in Pilates' court. This is in a temple in Jerusalem, according to verses 22-23. Then, in 39-40 it says they tried to arrest him but he ran away to Jordan. So he seems willing enough to say he's the Son of God... until he's directly asked by Pilates while on trial. Then he won't say it, which is why Pilates doesn't get involved.