WILMINGTON, Del.—Jurors heard opening arguments in the federal gun case for President Joe Biden’s son Hunter on June 4, with prosecutors focusing on self-admissions of drug use and bank statements they say implicate Mr. Biden in the alleged crime.

Prosecutors argue that Mr. Biden was, by his own admission, actively using crack cocaine between 2015 and 2019 when the firearm purchase was made and, therefore, lied on his federal application form. They also scrutinized pages of bank statements that show he withdrew roughly $399,000 in cash in 2018 alone.

The defense acknowledges Mr. Biden’s drug use before and after the purchase but maintains he was in “denial” about being a drug addict at the time. If, in his mind, he was not a drug addict when he filled out the form, he could not have lied, his attorneys argue. They also say his cash withdrawals were required to pay for rehab stints.

Mr. Biden is facing three felony charges from an Oct. 12, 2018, firearm purchase. Authorities accuse him of lying to the federally licensed gun store by illegally claiming on his application that he was not a drug user at the time and then unlawfully possessing the gun for 11 days.

Prosecutors discussed the events leading up to Oct. 12, 2018, when Mr. Biden purchased the .38 special revolver. His girlfriend at the time, Hallie Biden, widow of deceased brother Beau, threw the gun away after she found it in his car. Mr. Biden owned it for 11 days.

Prosecutors played audio excerpts from Mr. Biden’s self-narrated memoir that details his crack cocaine use between 2015 and 2019. At one point, Mr. Biden said he was up smoking crack every 15 minutes, seven days a week and called his ability to find the drug anywhere a “superpower.” He said he slept roughly 10 hours a week, on average, and lived in $59-a-night motel rooms while in the throes of addiction.

The defense claimed that it’s impossible to be a “functional” crack cocaine addict, suggesting that if Mr. Biden was functioning enough to communicate with family and purchase a gun, then he could not have been an “addict” at the time of the sale. Prosecutors then pinpointed a memoir excerpt where Mr. Biden said he was a “functional abuser” of the drug.

Prosecutors called FBI Special Agent Erika Jensen, who was assigned to Mr. Biden’s case, to testify. The FBI took roughly 18,000 pages of data from Mr. Biden’s iCloud account, including text messages, photos, videos, and WhatsApp messages, and compressed it into 75 pages of evidence for the court.

Videos and photos depicted alleged drug use, including images of a white substance on a green card and on a scale. In an August 2018 message, Mr. Biden talked about his “hope of getting clean” before he reportedly entered rehab. Prosecutors also highlighted a day in February 2019 when Mr. Biden’s phone had 62 messages about drug deals alone.

They also referenced a text message he sent close to the gun purchase where he asks the recipient, “Can you get baby powder, the really soft stuff?” which prosecutors say is coded language for cocaine.

During the prosecution’s afternoon presentation, Mr. Biden’s sprawling cash withdrawals came into focus. Bank statements show he withdrew roughly $399,000 in cash in 2018 alone, including $151,640 between Sept. 18, 2018 and Nov. 18, 2018. Prosecutors also reviewed statements showing a $5,000 withdrawal on Oct. 5, 2018, and another on Oct. 12, 2018, the day he purchased the gun for $886.81.

Mr. Biden’s defense attorneys claim he did not lie when he purchased the gun because he did not believe he was a drug addict at the time, alleging that he had gone days without using the drug.

While prosecutors acknowledged he entered rehab in August 2018, they quoted his memoir, where he claimed to relapse after leaving rehab. His attorneys argue the cash withdrawals were needed to pay for rehab.

Prosecutors pointed out that the leather gun case had cocaine on it when police found it, but the defense said the drug traces could have come from Ms. Hallie Biden or another source after it was thrown out.

During their opening remarks, Mr. Biden’s attorneys appeared to stumble and lose their place multiple times while maintaining his innocence.

Mr. Biden has pleaded not guilty and argues the Justice Department is unfairly targeting him after Republicans labeled his failed plea deal a form of special treatment due to his father’s position as president.

Mr. Biden will also face a September trial in California over his failure to pay $1.4 million in taxes. That case would have also been resolved through a plea deal in July 2023 before it eventually fell apart.

Mr. Biden is facing up to 25 years in prison if he is convicted in the federal gun case, although first-time offenders typically receive less than the maximum sentence. It is also unclear if the judge will give him prison time.

Joseph Lord and The Associated Press contributed to this report.