Can I bake a cake in a toaster oven without temperature control?
In general, yes.  But it's going to take a bit of effort and monitoring.

Your results may not be ideal (in particular don't expect the highest rising cake or the most even doneness), but it is possible to bake a cake in something like that.  There are three main issues:


The device you linked looks like it doesn't have temperature control.  It looks like it just turns elements on the bottom and/or top on and off.  So, you'll need to regulate the power yourself, turning the power off before the oven heats up too much and turning it back on when it starts to cool down.  If you're not experienced with baking without a built-in oven thermometer, you might want to try to pick up a cheap thermometer which you might be able to fit inside and help regulate temperature.
If there are electric heating elements on the top and bottom, they may be much closer to the cake than they would be in a larger oven.  That could lead to excess browning on the surface and/or the bottom of the cake.  You may need to bake at a lower effective temperature to avoid browning or even burning the crust.
The heat produced will be more uneven in general than a large oven.  That may interfere with rising or doneness in the cake.  There's not much you can do about that other than monitoring and making sure the cake is cooked through before removing.


I personally wouldn't recommend trying this unless you already have experience baking/cooking with this appliance.  Cakes are bound to be more sensitive to things like temperature fluctuations and radiant heat than many other things you might cook in such an appliance.  But if it's your only option, it may be workable.