Yes, both are correct. But they have different meanings. I'm on my phone so it's difficult to write a lot. "to spend Ving" means you're spending a period of time performing an action. You could also be spending money or something of value in order to perform an action. Ex. I spent my entire summer sleeping./Are you really going to spend the rest of college working full-time? Ex. He spent his entire allowance eating at that new restaurant. (Used with time phrases and monetary phrases). "To spend on" would usually be used with a noun but it could be used with Ving (if the verb is being used as a noun). I feel like not a lot follows the noun or verb. Ex. Don't spend so much on those new shoes. Don't spend so much on getting those new shoes. Don't spend so much on getting those new shoes.... All of these are natural and correct. Shorter is usually best in casual language because all languages like to be short and sweet and lazy. Thus, we may tend to omit "on" colloquially. Ex. You spent all of our grocery money on bowling?! (You could omit "on"). The difference is that using "on" makes bowling feel more like a noun. The game of bowling. The act of bowling. Omitting "on" makes it sound more like an action. The active process of a rolling a ball towards pins.