Solidity: View/Pure Gas usage

 As I understand,

Pure and View functions don't cost any gas to call if they're called externally from outside

In this type of case, there won't be any transaction initiated because this will be like just querying the blockchain for its current state and nothing will be changed.

But they do cost gas if called internally by another function.

This means there's already a transaction to change the state of the blockchain, and that process of changing state need to use that pure function, say for calculations. Gas cost for a transaction depends on the number of EVM opcodes executed while completing it, so executing that pure function is also within that set of opcodes. That's why it's said that it costs gas.

Consider the following contract:

pragma solidity ^0.4.24;


contract PureFunctionTest {

   uint state;

    function addNumbers(uint a, uint b) public pure returns (uint) {
       return a +b ;
   }

   function updateState(uint a, uint b) public {
       
     uint c = addNumbers(a,b);
     state = c;
   }

   function addThreeNumbers(uint a, uint b, uint c) public pure returns (uint) {
       
       uint temp = addNumbers(a,b);
       uint num  = addNumbers(temp,c);
       return num;
   }
}

Just calling addNumbers won't cost anything. But calling updateState will cost including cost to addNumbers(a,b) as well. Calling addThreeNumbers won't cost gas even if it called addNumbers internally since no transaction is needed throughout the function call.

References:

https://ethereum.stackexchange.com/questions/52885/view-pure-gas-usage-cost-gas-if-called-internally-by-another-function?rq=1 

In solidity, only making transaction will cost you gas. If you just directly call view/pure function, it will not cost you any gas.