Suppose that we consider English alphabets so we have 26 letters which 5 of them are vowels. I want to find all three letters sequences that contain at least one vowel.

My first approach is $26^3-21^3=8315$ which is the number of all three lettres sequences minus the number of three letter sequences which do not contain vowels. 

Second approach: at least one vowel means one vowel or two vowels or three vowels so the answer is $(5\cdot21^2)+(5^2\cdot21)+5^3=2855$.

Why are these two answers different?