I've never seen an LM7803 before. I assume you're talking about a linear regulator, like the LM7812 but set to 3V.
This will not work for a couple of reasons:
LEDs are designed to work from a constant current source, not constant voltage. You need a current regulator, rather than a voltage regulator.
A linear regulator is very wasteful, the input current is the same as the output current so connecting 8 linear regulators, each drawing 1A, will draw 8A in total: a 3V linear regulator wastes 75% of the power supplied to it.
You ideally need a switched mode constant current regulator to power the LEDs.
You need a more powerful power supply. Although a switched mode power supply is typically 80% to 95% efficient so most of the input power is delivered to the load, you still need to make up for the 5% to 20% power loss so you need a power supply capable of between 25.2W to 28.8W.
I assume you're powering this from the mains? If so your best bet is to buy a proper mains powered LED driver.
Failing that, a crude solution is to connect two strings of three LEDs in series, each with a 3 Ohm resistor to your 12V supply. This is only 75% efficient but it's better than using 3V linear regulators.