If we search around, we find unscholarly sources like this one:

https://www.reddit.com/r/HistoryPorn/comments/6uksgp/former_third_reich_leaders_laugh_at_a_translation/

"Former Third Reich leaders laugh at a translation error during Nuremberg trials, 1945-1946"

Now, a source like this is alone not sufficient to establish this, but one should admit that the explanation is at least plausible.

We find further confirmation and elucidation in an interview by Richard Sonnenfeldt given to the Süddeutsche Zeitung on 25.04.2002 as retold in A. Wirsching, "Nürnberg Zwischen Reichsparteitagen und Nürnberger Prozessen" in A. Schmid, K. Weigand (eds.), Schauplätze der Geschichte in Bayern, 2003, p. 388:

"Göring laughed" - Richard Sonnenfeldt, the chief interpreter of the American prosecution at the Nuremberg major war crimes trial, remembered this well when he gave an interview to the Süddeutsche Zeitung in April 2002. Although the other defendants in Nuremberg laughed again and again, they mostly laughed about banalities, such as the accent with which the allied accusers pronounced their names. Göring, however, laughed even when films from the liberated concentration camps were shown, some of which brought tears to the eyes. Göring dismissed them as propaganda.

Then we have the psychologist Leon Goldensohn's notes about his conversations with the Nuremberg defendants published as The Nuremberg Interviews: Conversations with the Defendants and Witnesses, 2004. Göring tried to justify his behavior as follows (p. 115):

The atrocities are, for me, the most horrible part of the accusation in this trial. They thought that I took it lightly or laughed about it or some such nonsense, in court. That is definitely a mistake. I am the type of person who is naturally against such things and my own psychological reaction is to laugh or smile in the face of adversity. Perhaps that explains my attitude in court. Besides, I was not to blame for these horrors. It’s not just that I am a hard man because of my long experience in the army and in politics. It’s true that I saw plenty in the First World War and during the air raids and at the front in this war. But I was always a person who felt the suffering of others. To paint me as an unfeeling ogre who laughs in court at the atrocities is stupid.

And further (p. 133):

If I give vent to my spontaneous reactions — such as laughing at the Russians when they try to cross-examine, or, another example, when I laugh at evidence about the atrocities, which, as I explained before, is not meant because I think it is humorous but because it is my personality to laugh in the face of adversity — then Dr. Gilbert feels that I am making a mockery of the atrocities and they treat me like a naughty child. I am fully convinced that this trial is a mockery and that someday when you Americans have your hands full of Russian troublemaking, you will see me and my activities in a different light.

Another Nuremberg psychologist, Gustave Gilbert, reports various instances of laughter in Nuremberg Diary (1961), some examples follow.

P. 65:

As the film went on, the Reichstag was shown laughing as Hitler read Roosevelt's letter asking for peace. In the dock, Goering laughed again.

Pp. 151-2:

Afternoon Session: The Russians presented their atrocity film, a horrifying document of mass murder even more terrible than the one presented by the Americans. [I stood at Goering's end of the dock and watched the prisoners in the semidarkness during the showing of the film. Goering is tickled at the false start, as the film starts upside down and has to be readjusted; he covers his laugh with his hand, but looks around to see if the audience is laughing . . . The film starts again] . . . It shows the acres of corpses of Russian PWs murdered or left to starve in the fields where they had been captured; the torture instruments, mutilated bodies, guillotines and baskets of heads; bodies hanging from lamp-posts, found upon recapture of towns where the Gestapo had been active; the ruins of Lidice; women weeping over their dead—mass burial services; raped and murdered women, children with heads bashed in; the crematoria and gas chambers; the piles of clothes, the bales of women's hair at Auschwitz and Maidanek . . . [Goering keeps pretending to read a book through all this, yawning in boredom, occasionally making a sarcastic remark to Hess and Ribbentrop.]

P. 287:

Afternoon Session: [When the cross-examination started in the afternoon, the Goering clique showed extreme pleasure as Prosecutor Jackson began to show that Schacht was much more enthusiastically tied up with the Party accession to power than he had been willing to admit.] Then Jackson quoted to Schacht some excerpts of his speech of November, 1938, on the "Wonders of Finance." [Goering, Sauckel, von Schirach and the admirals looked at each other, nodded and winked. Goering nudged Hess and said, "Put on your earphones; this is going to be good." The military men and propagandists enjoyed Schacht's embarrassment over the evidence that he had contributed a thousand RM yearly to the Party after getting the golden Party badge. Goering laughed until he shook.] Then the prosecutor turned to the subject of Schacht's knowledge of the growing Wehrmacht, which was hardly reconcilable with his peaceful aims. [Goering was tickled, and told the others, "Now it comes out."] With reference to the Koenigsberg speech, Jackson pointed out, "You stopped the quotation just at the point where I get interested." Schacht laughed in good-humored embarrassment, saying that he naturally left the other parts for the prosecution to quote. [This brought a snicker from Goering. "He giggles just like an innocent girl who's getting it for the first time!" He thought that was pretty good and repeated it to the boys in the back row.]

P. 327:

In the course of the cross-examination by the Russian prosecutor, General Alexandrov, von Schirach stated that his Hitler Jugend was far behind the Russian Youth in military training. [Frank laughed until he was red in the face.]

P. 355:

Von Papen also considered the waging of war against Russia a crime. He described a plan in which he was supposedly involved to surround GHQ and capture Hitler to bring him to trial. His attorney then submitted an affidavit by Bismarck's grandson showing that von Papen was thought of as Foreign Minister by the July 20 plotters. [Goering laughed and shook his head. Jodl turned red and looked as if he was seeing red.]

P. 356:

Afternoon Session: Upon cross-examination, Sir David Maxwell-Fyfe embarrassed von Papen by quoting back to him his own speeches in which he called Hitler as heavensent to the German people to lead them out of their misery. [Goering laughed and all but thumbed his nose at von Papen. ...]

But in the end (p. 392):

Goering acknowledged defeat on the psychological front: "You don't have to worry about the Hitler legend any more," he said despondently. "When the German people learn all that has been revealed at this trial, it won't be necessary to condemn him; he has condemned himself." As the day of sentencing approached, he grew more and more nervous and found it harder and harder to laugh.