I am a diabetic and i wanted to find out why my big toe nail is darkening in color from about 3 weeks now.

Diabetes & toes: Recommend that diabetic patients have a foot examination at least annually. Recommend podiatry eval and the toe nail can be assessed at that time.

Nail pressure?: If the dark color is only affecting the nail of one toe it could possibly be due to pressure on that toe from a shoe that is too tight (bruising or blood under nail) :consider a change of shoes. But there are other skin problems that can occur under the skin so if you change shoes & nothing improves you should see Dr

Injury?: since one of the effects of Diabetes is peripheral neuropathy ( this reduces feeling and blood flow) it is common to injur yourself and not feel it and then the decreased blood flow results in a much longer healing time. See PCP or podiatrist to monitor, this can be a big problem if blood flow is too limited and things not monitored gangrene can result and people loose toes