Basically, the opposite of all the usual times when Darth Vader speaks of Anakin Skywalker. "The apprentice of Anakin Skywalker" "The son of Skywalker" "Anakin Skywalker was weak, I destroyed him" and so on so forth.
In general it is difficult to tell whether Vader is speaking of Anakin or Vader when he says "I...", even when he's talking about the past. For example, while dueling Obi-Wan on the Death Star Vader tells him:
When I left you, I was but the learner; now I am the master.
Star Wars: Episode IV A New Hope
Vader could be referring either to Anakin the Jedi who left Obi-Wan (once he was no longer a padawan) or Vader the newly minted Sith Lord who abandoned the Jedi and Obi-Wan. It depends on when in the past Vader is saying he "left".
Despite that difficulty, I think the best case of Vader referring to Anakin occurs when Vader reveals Luke's paternity:
Vader: If you only knew the power of the dark side. Obi-Wan never told you what happened to your father.
Luke: He told me enough! He told me you killed him.
Vader: No. I am your father.
Star Wars: Episode V The Empire Strikes Back
If Vader and Anakin are different persons (as Vader likes to believe) then Vader is not Luke's father. Luke was conceived before Anakin became Vader so only Anakin can be considered Luke's father. Vader can't be thinking of Luke as some sort of evil son of Darth Vader, either, because Vader is attempting to recruit Luke to the dark side. By saying "I am your father" Vader is implicitly admitting that Vader and Anakin are the same person. Furthermore, when Luke says that "Vader killed Anakin" Vader repudiates it with a firm "No" -- but that's the idea which allows Vader to think of himself as a different person from Anakin in the first place!
Vader makes another, similar slip-up when he tells the Emperor:
My son is with them [on the forest moon of Endor].
Star Wars: Episode VI Return of the Jedi
And again, Vader slips and calls Luke his son when he meets Luke on the forest moon of Endor:
It is too late for me, son.
Star Wars: Episode VI Return of the Jedi
Numerous times, Vader associates himself with Anakin in the context of Luke. This is important because it was Vader's love for his son which turned him back to the light side. As Luke had pointed out, Vader is still Anakin but had "only forgotten" it (or attempted to forget it).
Occasionally, but with less frequency later on
Vader generally tries to deny his past as Anakin, but there are some times when he is willing to admit it. In the canon novel Lords of the Sith, for example, he admits that he went to Ryloth as Anakin (as described in The Clone Wars):
“You have been to Ryloth before, have you not, Lord Vader?”
The question dredged memories of war from the depths of Vader’s mind.
“Long ago, Master. Before I learned wisdom.”
Here there is an implicit “I,” i.e. “I went to Ryloth long ago,” as well as perhaps an explicit one in Vader’s reference to learning wisdom.
Later, he seems to reference his love for Padme:
She stared up at Vader, unafraid. “I hate you and everything you stand for,” she said. “But when I murdered, I murdered out of love.”
Vader raised his blade, his breathing loud and steady. When he spoke, his voice was as deep and hollow as a funeral gong.
“I know precisely what you mean,” he said, and slashed.
In this place, “I” surely references what Anakin felt for Padme.
Vader sensed the anger in his Master, sensed, too, the threat that lived in that anger. Vader did not fear it, not at that moment.
“Where are the guards?” he asked. The Royal Guards were nowhere to be seen. “How long was I…”
“I sent them away. They will return soon.” A long silence, then, “What did you see as you meditated?”
“I saw…deaths, and faces from my past, the events that led me to this moment. I see them frequently when I consider the destiny the Force has for me.”
When he speaks of “my past” here, he is recalling such events as killing Dooku, or Mace Windu’s anger at his betrayal, events that occurred before he was Vader.
Indeed, the story of Lords of the Sith is to a large extent that of Vader learning to leave behind his ties to his previous life. By the time of Tarkin, Vader has begun rejecting his past even to Darth Sidious:
“Then you know what that world is like. Venture outside the safe haven of Eriadu City and the land is every bit as bleak and hostile as Tatooine. That land forged Tarkin in much the same way Tatooine forged you.”
Vader shook his head. “Tatooine did not forge me.”
Sidious stared at him, then grinned faintly. “Ah, I see. Slavery and the desert forged Skywalker. Is that what you mean?”
By the time of the original trilogy, Vader has entirely separated his current self from his past as Anakin—until Luke starts to redeem him, in any case.
It might help to note that once Vader found out that his son, the last remnant of Padme, was alive, the call to the light grew within him. Luke even stated in Return Of The Jedi, "I can feel the conflict within you. Let go of your hate!" Vader was still trapped within the Dark Side, but Anakin was very much alive and returned from the ashes of Mustafar once the only piece left of Padme was right in front of him.
Vader was saying "I..." in reference to his life as Anakin due to his internal conflict. Anakin was shining through because Luke was a reminder of Padme, the only reason Anakin became Vader in the first place. Sidious lied to Vader and said Anakin killed Padme, which Vader resented and hated Sidious for, but his life was cemented in the Dark Side because Sidious was all he had left of his former life, or so he thought. A strong surge in the light side of the force was felt by both Vader and Sidious, but it was Sidious who identified the force presence as Luke Skywalker, son of Anakin Skywalker. This initiated the conflict within Vader and deepened his hatred for the Emperor.
The complete redemption of Vader came when he saw that he would have to kill Luke, thus completely killing Padme. The thought of killing any part of Padme was devastating and he couldn't bring himself to do it, because even after all the years of mental torture he endured, he was still in love with her. That is why Sidious attempted to kill Luke, but the more Vader thought about killing his son, whom he loved, and completely destroying Padme forever, the more he wanted to kill Sidious for destroying his life. That is when Vader ceased to exist and Anakin returned.