At the ripe old age of 94, Warren Buffett is finally getting ready to hang up his investing boots, having announced his retirement by the end of the year last weekend. But that hasn't stopped him from amassing a war chest for the ages at his company Berkshire Hathaway Inc (NYSE: BRK.A)(NYSE: BRK.B).

According to CNBC's Berkshire portfolio tracker, Buffett, as of 31 March, has US$347.7 billion in cash and cash-equivalent investments ready to go at Berkshire. That cash pile is worth more than the combined public stock portfolio of Berkshire right now (although not if combined with its private, unlisted investments). It's also the highest cash position Berkshire has ever had. Not a bad problem to have, all things considered.

But let's move from the factual to the hypothetical. If I had a cash pile as large as Warren Buffett's, what would I spend it on?

Well, apart from a nice house and perhaps a vintage Aston Martin DB5, I would, of course, buy stocks.

The ASX shares I would buy with Buffett's cash pile

I would be happy to spend a large chunk of the pile on a simple index fund tracking ASX shares, probably the Vanguard Australian Shares Index ETF (ASX: VAS). This exchange-traded fund (ETF) offers investors exposure to the largest 300 shares listed on the ASX, weighted by market capitalisation.

This is a great hands-off investment that will likely grow in line with the broader Australian economy over time, which I find appealing as a cornerstone investment.

Following VAS, I would then opt for some additional ASX shares that balance a supply of reliable dividends with some of the ASX's most exciting growth stocks.

For dividends, I would choose a mixture of Washington H. Soul Pattinson and Co Ltd (ASX: SOL), Coles Group Ltd (ASX: COL), Telstra Group Ltd (ASX: TLS), Wesfarmers Ltd (ASX: WES), and National Australia Bank Ltd (ASX: NAB). These companies all have a strong history of providing hefty and steadily rising dividends, which is a trait Buffett himself often looks for.

I would add investments in TechnologyOne Ltd (ASX: TNE), REA Group Ltd (ASX: REA), and Xero Ltd (ASX: XRO) for some growth exposure too.

Never bet against America

But I wouldn't just stick with ASX shares. Warren Buffett himself has expressed his belief that the US markets, and the companies that reside on them, are the world's best. As such, I would probably invest more of that enormous cash pile into US stocks than those on the ASX.

My top priorities would be the companies that are leaders in their fields and have a long history of delivering for shareholders. I would start with the magnificent seven stalwarts Amazon.com Inc (NASDAQ: AMZN), Alphabet Inc (NASDAQ: GOOG)(NASDAQ: GOOGL), and Microsoft Corporation (NASDAQ: MSFT). I think these names are the best that the US currently has to offer, and have long growth runways still ahead of them.

Then, I would add quality names like Mastercard Inc (NYSE: MA), Netflix Inc (NASDAQ: NFLX), American Express Inc (NYSE: AXP), and Costco Wholesale Corp (NASDAQ: COST).

Perhaps I would also consider Caterpillar Inc (NYSE: CAT), McDonald's Corporation (NYSE: MCD), and Procter & Gamble Inc (NYSE: PG).

With these stocks, which range from growth engine companies like Mastercard to consumer staples fortresses like Procter & Gamble, I think I would have a portfolio that could look after my family's financial interests for the rest of my days.

Shame about the lack of a Buffett-style cash pile, though.

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