You could and I have heard this, but it would be better to use the correct adjective: "sunny" to describe the day, e.g: "It's really sunny today."
The reason is that "sun" is not a measurable quantity. A "sun" is a countable noun, and for the same reason you would never say "There is a lot of dog", instead "There are a lot of dogs."
"There is a lot of water" is OK, because we measure water. One can measure "sunlight", so theoretically "There is a lot of sunlight" is correct, but it sounds unnatural unless you are describing something like the interior of a house where people normally check how much sunlight comes through windows ("Ah, this room has a lot of [sun]light!"). Sometimes people use the word "sun" as if it were an uncountable noun meaning "sunlight", and that's when you may hear "There is a lot of sun". This arguably is substandard language, but it wouldn't be difficult to understand.