Canon MultiPass MP360 Printer - I have changed the black-ink cartridge but it still won't print out black ink?

I have changed the black-ink cartrige 3 times & reset the ink-counters. I have also tried printing out documents many times, but the black-ink parts don't show up at all. I have tried deep-cleaning, print-head-alignment & nozzle checks, but it doesn't work. The colours are printing out fine, but the black... show more I have changed the black-ink cartrige 3 times & reset the ink-counters. I have also tried printing out documents many times, but the black-ink parts don't show up at all. I have tried deep-cleaning, print-head-alignment & nozzle checks, but it doesn't work. The colours are printing out fine, but the black ink isn't - any ideas?

Thanks in advance
Update: 'Smedrik', yes we have used a 3rd party cartridge & will definitely try what you recommend - thanks
Update 2: Thanks to Bob P as well
Update 3: thanks elly r, will try!
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