To begin, what you are describing are 3-way switches if you have two switches controlling the same light from different locations. Pull out the switches and check the wiring. These switches should have three wires attached to them perhaps two blacks and a red or a black, red and white. At the very least, one of the switches is wired incorrectly. However, none of this explains only two blacks being attached to the fixture unless you have old style wiring where it appears both wires are black but actually one has a faint strip which is the neutral. All of this is spectulation with limited information.

its sounds like its range wire. if it is range wire, or 8-3, that means it has 3 8 guage wires and a number 10 ground, it also has a black outer sheathing. i have never seen solid 8-3 romex before though, its typically stranded. if in fact it is 8-3 then it is good for 40 amps. if its in an existing house you should try to check the breaker that its connected to. if youre still sketchy you can buy things that tell you the size of the wire. it has holes in it for all sizes of wire so you just stick the wire through the holes to find which one it fits best into. hope this helps.

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Brown is hot (black or red in US/Canada), and blue is neutral (white or grey in US/Canada). Be careful. That color code (EU/UK/China standard) is a warning sign that the fixture isn't designed or approved for use in the US or Canada. It's a good bet that you have a directly imported Chinese item there, If so, it probably doesn't have UL approval. If you seller even bothered to slap a UL symbol on it (most don't), the symbol may be counterfeit. Your gadget may even be unsafe. It's true that most of the lighting items sold in the US are made in China, but you can be pretty sure that the ones sold by brand name companies with reputations to protect have been checked for quality, and tested to UL or equivalent standards. They have standard US/Canada color codes, too. Name brand fixtures cost more than the no-name cheap junk from the big auction place and the big e-commerce website, but how much is your family's safety worth?