There is no set cost to running a Bitcoin node. While the software for running a node is free and open source (as per the guidelines of a decentralized cryptocurrency), the main cost comes from the computer, hard drive, power supply, and internet connection you need to run a Bitcoin node.
To successfully run a Bitcoin node, you generally need 125 GB of free disk space, 2 GB of RAM, a broadband internet connection with upload speeds of at least 50 KB per second, and a connection with sufficient download limits.
While some users have managed to run a Bitcoin node with cheaper hardware when working out how much it will cost you to run a node, remember to account for the cost of higher utility bills and potentially exceeding your network usage limits.