A few questions to clear things up. What kind of LED's? Is this a string of LEDs like a rope
light or individual LEDs? What is the operating voltage of the LEDs? From your calculations it looks like 12V , if so why the car inverter?
As StuM pointed out a 40W panel would be best and unless you use an MPPT
controller with the panel the full rated wattage will never go into the battery, but now were talking some serious $$$.
Don't know your application but how about this? I'm using a string of outdoor solar holiday LED lights
for cockpit lighting
, turns on at dusk and off at dawn, comes wired to a 4x4" box that has the solar panel, batteries and light sensor. Not very bright though, but it was less than $10 on Amazon.
Hope that helps.