때문에 or 이라서 should be inside the sentence for linking the noun, gerund and conneting the two sentences. 빅뱅은 내(나의 my) 좋아하는 그룹 때문에 그들의 음악은 좋다고 그들은 너무 멋져! I'd change your sentence like this with a little correction. :빅뱅은 내가 좋아하는 그룹이기때문에/그룹이라서 그들의 음악은 좋고 그들은 너무 멋져! =빅뱅은 내가 좋아하는 그룹이야. 그래서 그들의 음악은 좋고 그들은 너무 멋져! (I can make it more idomatic and natural than this sentence, but I prefer making the sentence like this way for your learning.) Bigbang is my favourite group because their music is good and they are so cool! It's just a matter of each person's preference or choice. I would say I like BIGBANG because they have a talent and know how to enjoy the stage. And the best thing is the fact that they are true musicians.

Here's another version. 빅뱅은 내가 좋아하는 그룹이야 Bigbang is my favourite group / 왜냐면 빅뱅 오빠들(I think you're younger than the members, so.. :) 음악이 좋거든 / They are so cool! 빅뱅 오빠들 짱 멋있어!

i always say 왜냐하면/왜냐면..... 왜냐하면, bigbang의 음악은 최고입니다, 그리고 그들은 멋져요.. hehe

your sentences don't sound right to me, but I'm just learning myself, so I don't want to give you potentially wrong answers, you can check these websites until someone more knowledgeable can answer you: http://parksguide.blogspot.com/2009/06/conjunctions-because.html http://www.talktomeinkorean.com/lessons/level-5-lesson-14/ http://www.talktomeinkorean.com/lessons/l6l17/