1
He died of a liver cancer.
He died of liver cancer.
When we simply name the disease, we normally use cancer without a or an: liver cancer, skin cancer and breast cancer.
We can use a cancer when we mean one particular type of cancer: ‘This is a rare cancer that mainly affects children.’
2
I hope we find a cure for the cancer.
I hope we find a cure for cancer.
Do not use the with cancer when talking about the disease in general.
Use the cancer when referring to a particular cancer: ‘The cancer has spread to John’s lungs.’
The same pattern is common with many other diseases: ‘She has diabetes.’ ‘He is being treated for pneumonia.’ ‘Malaria is common in some tropical countries.’
See THE (2)