Could i enter at Harvard university with out a high school diploma the age of 21?

No, you cannot enter Harvard University without a high school diploma, even at the age of 21. While Harvard accepts students of all ages and backgrounds, a high school diploma (or equivalent like a GED) is a fundamental requirement for admission. They might consider exceptional circumstances, but these are extremely rare and would not involve bypassing the requirement altogether. Harvard's admissions process is highly competitive even for applicants with high school diplomas.