"Because" and "because of" are both used to introduce reasons.
"Because" is a conjunction and is followed by a subject and verb.
conjunction = a word such as "and", "but", "nor", "while" or "although", that connects words, phrases and clauses in a sentence. In the sentence "I like coffee, but I don't like tea." "but" is a conjunction.
"Because of" is a preposition and is followed by a noun phrase or verb-ing.
preposition = a word which is used before a noun, pronoun or noun phrase to connect it to another word. In the sentences "She sat on the chair." and "He walked along the street" "on" and "along" are preposition.
"I couldn't go out because I had a cold."
Did you see the subject and verb after because? She said "I had a cold."
"I couldn't go out because of my cold."
Did you catch the noun phrase? - "my cold"
You could also use a gerund - that's a verb plus "ing" after because of .
"I couldn't go out because of having a cold."
A verb with "ing" often functions as a noun so you use it after "because of."