There hasn't been reports of cancer transfer through blood transfusions (very rate and if any) but there are reports from solid organ transplants.

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The first thing is what exactly is cancer. Cancer is still a mystery to scientistic/medical community.

In simplest terms cancer is your own cells running amok. Obviously there is a "switch" that as your organs form it knows to stop dividing. For example, imagine if your heart cells, in utero forgets to "turn" off and keeps dividing. Somehow, it knows once it forms a "heart" it stops dividing.

Cancer cells do not know how to turn itself off. It keeps dividing and growing.

So to answer your question, can a transfusion spread cancer to another person. It is the so call "switch" that has become elusive in science. You would need to transfer whatever triggers the cancer cell from the donor body into the host body and the host cells would then need to incorporate it.

NFκB is an important signaling pathway that is involved extensively in cancer development and progression. The protein molecule has been studied at least over a decade. But simply blocking it does not necessarily prevent/treat cancer but research is ongoing.

However, we also know that some viruses can "spread" cancer like HPV. The human papilloma virus, which is associated with cervical and head and neck cancers, encodes a protein, E6, that promotes degradation of p53, while another viral protein, E7, inactivates pRB and CKIs, among other effects (Munger and Howley 2002). However, HPV is spread person to person through contact.

Hepatitis B can cause liver cancer and is spread through blood.