I got something like this:

cur.execute("INSERT INTO name VALUES(HERE_IS_VARIABLE,'string',int,'string')")

Stuff with %s (like in python 2.*) not working.
I got errors, which tells me that im trying to use "column name" in place where i put my variable.
You can try using f-Strings and separating out the statement from the execution:
statement = f"INSERT INTO name VALUES({VARIABLE_NAME},'string',int,'string')" 
cur.execute(statement)
You might also want to try with '' around {VARIABLE_NAME}: '{VARIABLE_NAME}'
In f-strings, the expressions in {} get evaluated and their values inserted into the string. 
By separating out the statement you can print it and see if the string is what you were expecting. 
Note, the f-string can be used within the cur.execute function, however I find it more readable to separate out. 
In python3.6+ this is a better way of formatting strings then with %s. 
If this does not solve the problem, more information will help debug:
what is the name table's schema?
what variable / value are you trying to insert?
what is the exact error you are given?
Python3.6 + Postgresql how to put VARIABLES to SQL query?