Can cancers caused due to viruses be contagious?
The question title and the question itself ask two slightly (but critically) different questions. 


Can cancers caused due to viruses be contagious? NO
Are these oncoviruses infectious in nature? YES


The tumors caused by the viruses are not contagious.  You can't take the tumor and transfer it to a new host and see a new cancer.  The viruses that cause the tumor are contagious, but in many cases by the time the tumor has arisen the viruses are no longer in a contagious form.  A tumor that's caused by HPV doesn't have contagious virus in it (see explanation below), and you can't transplant the tumor into a new host.  There still may be contagious virus present in the patient, but the tumor itself is not contagious.  

Explanation HPV causes cancer by having a part (and only a part) of its genome integrated into the host genome, so cancers associated with it inevitably have a defective virus genome. There could theoretically be infectious virus in the neighboring tissues, but the cancer is driven by non-contagious virus. See for example The role of integration in oncogenic progression of HPV-associated cancers for a fairly basic explanation