Sqlite insert query not working with python?

You do have to commit after inserting:

cursor.execute("Insert into links (link,id) values (?,?)",(a,b))
conn.commit()

or use the connection as a context manager:

with conn:
    cursor.execute("Insert into links (link,id) values (?,?)", (a, b))

or set autocommit correctly by setting the isolation_level keyword parameter to the connect() method to None:

conn = db.connect('insertlinks.db', isolation_level=None)

See Controlling Transactions.