While it is theoretically possible for a red velvet cake to cause a change in the color of the water in the toilet, it would be highly unlikely under normal circumstances.
The red color in red velvet cake comes from a combination of cocoa powder and red food coloring. In most recipes, the amount of food coloring used is relatively small, and it is mixed with other ingredients in the batter. During the baking process, the food coloring is distributed throughout the cake, resulting in a reddish-brown color.
Once the cake is baked, it is consumed as food, and its ingredients are broken down and digested like any other food item. The food coloring used in commercial products is generally safe for consumption and approved by regulatory authorities.
For the color of the water in the toilet to change significantly, there would need to be an excessive amount of undigested food coloring passing through the digestive system and into the waste. This is highly improbable with a regular serving of red velvet cake.
However, in some rare cases, consuming large quantities of certain food dyes or food with concentrated artificial colors might result in subtle changes to the color of urine or feces. For example, consuming large amounts of foods with natural red pigments like beets or artificial dyes like those found in brightly colored candies might lead to changes in urine color, but it's generally harmless and temporary.
If you notice any significant and persistent changes in your urine or feces color after consuming certain foods, it's always a good idea to consult a healthcare professional to rule out any potential health concerns. But for the most part, red velvet cake is unlikely to turn the water in the toilet red.