Not sure why you are saying Berkshire doesn't own publicly traded companies like AAPL. If you google "how much apple does berkshire own," you will see that Berkshire does indeed own publicly traded AAPL shares, and they are currently valued at $157 billion.
The guy said "not only public companies"! Berkshire is not only having hundreds of billions in stocks they have hundreds of billions in businesses they own. The reason they were able to invest in Coke or American Express is decades ago, their insurance business threw off massive cash so reinvested. They bought, a railroad for $30-$40B, a decade ago, they bought some lubricant company for $10B, a decade ago. They own like Century 21 and it's under their Berkshire Homes division. They own Dairy Queen and I think Fruit of the Loom. They're also sitting on around $150B in cash.
You are right, Google is showing BRKA market cap as $750B. But I don't understand that. If you google how many shares exist of BRKA, it says 620,000 shares. Multiply that times today's closing price of $514,000, and you get $320B, not $750B. I'm lost, lol. How is google getting a market cap of $750B?
Berkshire Hathaway has A and B classes of common stock. https://finance.yahoo.com/quote/BRK-A/key-statistics?p=BRK-A with 615.33K shares outstanding * $512,991 close price = $315,658,752,030 https://finance.yahoo.com/quote/BRK-B/key-statistics?p=BRK-B with 1.29B shares outstanding * $342.41 close price = $441,708,900,000 $315,658,752,030 + $441,708,900,000 = $757,367,652,030