I was wondering if there is a test or way to find out how sweet any drink is? For example, if I mix sugar in water, how can I test its level or number of sweetness?
As asked by the OP, I think the answer to the question has to be no. If it was known that a drink contained only glucose as a sweetener, then it would presumably be possible to measure accurately the glucose concentration in the drink. But maybe other substances in the drink would be interferences in the measurement. Following on, as @Alchimista commented, perhaps a Scoville-type sweetness test could be used. But the possible interferences problem complicates this as well. In addition, perceptions of sweetness may also be affected by seemingly innocuous substances in the drink, e.g., I find that a dash of table salt makes watermelon taste sweeter and I have no clue how that might arise.
Then there is the matter of inorganic substances. The old fashioned name for lead acetate was ‘sugar of lead’. Poisonous though it is, it earned its deadly sweet name. As well, some salts of beryllium ('glucine'; all berylium salts are highly poisonous) and yttrium are sweet tasting: see wiki. So it is not just various organic substances that can taste sweet and who knows what else is sweet tasting: no sane chemist (nowadays) tastes chemical substances.
My guess is that there are quite a few chemicals that would taste sweet, but we will probably never know what they are. Then how would sweetness levels of two lead acetate aqueous solutions be compared? I don’t see how it can be assumed, a priori, that sweetness is directly proportional to lead ion concentration and no one should do such an human subjects experiment anyway. And what about a drink containing glucose and lead acetate? Even if the lead acetate did not interfere with the quantification of the glucose concentration, the drink would be sweeter than expected from just the glucose measurement result.
if I mix sugar in water, how can I test its level or number of sweetness?
Number of sweetness is perhaps subjective. However, sugar content can be measured by refractive index changes (if you are just talking about sugar and water and no colors). Refractive index linearly increases with sugar content in water.
Keep in mind it is not a highly selective test but it quite routinely used as well. You need a refractometer for that purposes.
Another simple test is density measurement for sugar content, and there is a special unit. Read more about Brix unit elsewhere.