The BBC reported details of the leaked letter on Monday and McLaren confirmed they were correct.
Championship leaders Red Bull, who won the drivers' title last year and this with Max Verstappen, breached the $145million cap in 2021.
The FIA said on October 10th that it was a 'minor overspend', or less than 5% of the overall cap, but gave no details of how much was involved. Red Bull have said their submission was below the cost cap limit.
Brown did not directly name Red Bull or Aston Martin, who were deemed to have committed a procedural breach, in the letter dated October 12th with copies sent to those other teams who complied with the financial regulations.
"The overspend breach, and possibly the procedural breaches, constitute cheating by offering a significant advantage across technical, sporting and financial regulations," he wrote.
"The bottom line is any team who has overspent has gained an unfair advantage both in the current and following year's car development.
"We don't feel a financial penalty alone would be a suitable penalty for an overspend breach or a serious procedural breach. There clearly needs to be a sporting penalty in these instances, as determined by the FIA."
Brown suggested a team in breach should have their cap cut in the year after the ruling with a penalty equal to the overspend plus a further fine - so a $2million overspend in 2021 would mean $4million less for 2023.
"In addition, we believe there should be minor overspend sporting penalties of a 20% reduction in CFD (computational fluid dynamics) and wind tunnel time," he added.
Brown also suggested changing the rules so any second minor overspend breach automatically became a major overspend, and lowering the threshold from 5% to 2.5%.
The American said the cost cap, introduced last year to help level the playing field, had been a key factor in attracting new shareholders and investors to Formula One.
"It is therefore critical that we be very firm on implementing the rules of the cost cap for the integrity and the future of F1," he wrote.
