Splenda doesn’t cause cancer, it’s not even classified as a possible carcinogen.
However *other* foods that are considered by science to be possibly/probably carcinogenic generally contain chemicals that are know to alter or otherwise affect human DNA.
There is no surefire “cancer chemical”, but carcinogenic chemicals essentially are able to do the biochemical equivalent of going into your cells and start flipping switches, or standing in the way when certain critical activities like DNA replication are taking place. Over time, a cell is more likely to become cancerous the longer it’s exposed to these effects.
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