Apdu commands and responses to what's going on

APDU write block commands based on mifare classic

I have already tried to write some data on my mifare classic cards. first i send these two commands which gives 90 00:

Load Mifare key:

FF 82 20 01 06 FF FF FF FF FF FF

Authenticate:

FF 86 00 00 05 01 00 01 60 01

now I can write commands to sector 0 and block 1 + 2

ff d6 00 01 10 14 01 03 E1 03 E1 03 E1 03 E1 03 E1 03 E1 03 E1

ff d6 00 02 10 03 E1 03 E1 03 E1 03 E1 03 E1 03 E1 03 E1 03 E1

I mistakenly overwritten block 3 a couple of times rendering this sector unreadable it seems:

when i send the command
ff d6 00 04 10 i get return error 69 82 which i googled like authentication error

do i need to authenticate to each sector? if so, what is the command to do this for the next and following sectors?