This idea that aspartame can cause cancer was due to a published paper that indicated a correlation between aspartame consumption and cancer in rats.  This study, however, has been called into question many times. For starters, animal studies do not correspond well to effects in humans. No consistent data in humans have been published indicating that aspartame is linked to cancer. Additionally, the rats were fed doses of aspartame high enough to be considered unsafe in humans. This isn’t exactly equivalent to having a diet drink every once and a while. 
Aspartame is an FDA-regulated food product. Its consumption is considered safe up to 50 mg/kg body weight per day. The European Union has a slightly lower safety measure at 40 mg/kg per day. To put that in perspective, if an individual weighs 150 lbs (68kg), up to 3,400mg of aspartame consumption per day is recognized as safe. Coke zero contains 58mg of aspartame per 8oz. That means in order to consume an unsafe amount of aspartame, that 150lb individual would have to consume about 58.6 8oz bottles of Coke Zero which is equivalent to 469 oz of the beverage. That’s a lot of diet soda!
Additional Concerns About Aspartame
Other than cancer, there have been a few additional concerns regarding aspartame. Some research has identified a potential link between aspartame consumption and sweet cravings, as well as alterations in the gut microbiome. For more information on this research and additional concerns regarding aspartame, check out our full article about aspartame.
Concluding Thoughts on Drinking Coke Zero on Keto