There's many sugar in the jar

The sentence should use "There are" instead of "There's" because "sugar" is a mass noun and the quantity is described as "many", implying a plural or uncountable quantity. Alternatively, if referring to multiple types or packets of sugar, "There are many sugars" could be used, but "There is much sugar" or "There is a lot of sugar" would be more common for a mass noun. Given the context of "in the jar", "There is much sugar" or "There is a lot of sugar" is the most likely intended correct form.