Unfortunately, I cannot give you the answer to that question, although the number must certainly be in the thousands. Part of the difficulty in answering this question is that there are many situations where farmers in different parts of a country will use a different name for the same variety. In order to confirm whether varieties are different or the same, it is therefore necessary to do genetic studies using techniques of molecular biology. I work on cassava viruses, so know something about the crop. However, I have colleagues that, if you are interested, I'm sure would be happy to give you more detailed information. Alternatively, you can check out the websites of the International Institute of Tropical Agriculture (IITA). www.iita.org or the International Centre for Agricultural Research (CIAT) www.ciat.cgiar.org
Thanks for the website about cassava, i will use as my resource about this species. The reason why I question about the variety of cassava is I have a plan to conduct a study about the morphological diversity of the cassava. :)