Tesla did $1.6 billion in regulatory credits in 2020. Tesla stock based compensation in 2020 was $1.7 billion due to Elon Musk's performance based compensation plan and TSLA skyrocketing. So the car business is clearly profitable.
Then there's the capitol expenditure on building out new factories and expanding their production capacity. From Tesla's 2020 Q3 10Q filing:
> we currently expect our capital expenditures to be at the high end of our range of $2.5 to $3.5 billion in 2020 and increase to $4.5 to $6 billion in each of the next two fiscal years.
They're planning on spending up to $12 billion between 2021-2022 to build out new factories and expanding their capacity. Their car business is clearly profitable, they're just spending all of the money to grow.