LeBron James -- 'FOR6IVEN' Shirts Explode ... Website Breaks from Traffic Eruption

A t-shirt website selling LeBron James "For6iven" shirts was bombarded with cyber-traffic in the moments following 'Bron's announcement ... breaking the site ... TMZ Sports has learned.

We spoke to the owner of Fresh Brewed Tees -- who tells us the demand for the shirts SKYROCKETED ... and in the first 5 minutes after the announcement, the site crashed due to a sudden influx of traffic.

The owner, Tony Madalone, says the site has only been selling the shirts for a few days -- but judging from the overwhelming interest, he expects to sell more than 10,000 shirts .