if you read what Jesus said a little earlier (chpt 5) you will find that he had already confirmed that God had been his witness along with John the Baptist...So he already had 2 witnesses beside himself as to his true identity. The powerful works he was performing by Gods power, and the testimony of John the baptist
John 5:31 If I alone bear witness about myself, my witness is not true. 32 There is another that bears witness about me, and I know that the witness which he bears about me is true. 33 YOU have dispatched men to John, and he has borne witness to the truth. 34 However, I do not accept the witness from man, but I say these things that YOU may be saved. 35 That man was a burning and shining lamp, and YOU for a short time were willing to rejoice greatly in his light. 36 But I have the witness greater than that of John, for the very works that my Father assigned me to accomplish, the works themselves that I am doing, bear witness about me that the Father dispatched me.
now come down a little to chpt 8 and you'll see that in context Jesus is not claiming that his testimony is all that is needed...he is reiterating the fact that he is speaking truth because the Pharisees continually harassed him over the things he was teaching
12 Therefore Jesus spoke again to them, saying: I am the light of the world. He that follows me will by no means walk in darkness, but will possess the light of life. 13 Hence the Pharisees said to him: You bear witness about yourself; your witness is not true. 14 In answer Jesus said to them: Even if I do bear witness about myself, my witness is true, because I know where I came from and where I am going. But YOU do not know where I came from and where I am going. 15 YOU judge according to the flesh; I do not judge any man at all.