I have found some sites stating:
Principal * Annual-Interest-Rate * Term-Length-Years
... but this does not calculate the total interest paid correctly. This formula neglects a shrinking principal balance. Also, I'm sure a working formula would depend on the compounding frequency as well.
How can one calculate the total interest to be paid on a loan? Does the loan need to be amortized to find this value?
An amortization schedule is effectively a detailed description of the terms for repayment of the loan, and there can be many variations in the loan agreement as to what the repayments are and what each penny of each repayment means. A common amortization schedule requires the borrower to pay a fixed amount at fixed times (typically monthly) and each payment consists of the interest accrued since the previous payment on the amount still owed, plus a partial repayment of the principal. Thus, the amount still owed reduces after each fixed payment, and so successive payments have less of accrued interest (the amount still owed is decreasing) and more partial repayment of principal. However, it is possible to have a loan agreement that specifies that all payments except the last payment shall be of only the interest accrued since the previous payment, and the last repayment shall be the entire principal amount plus the interest accrued on the principal for the time between the penultimate repayment and the last repayment, which is often referred to as a balloon payment. Regardless, of what the payment schedule is, the total interest paid is just
Sum of all the repayment amounts - Principal Amount
which can be calculated from the loan agreement and its attached schedule of payments. In practice, what you actually will have paid over and above the Principal Amount when the loan is finally paid off will depend on whether you have made all the loan repayments on time, any fines/penalties for late payments, whether you pay off the loan early or grind it out to the bitter end exactly as promised (after all, the word mortgage comes from the French and means a deathgrip on the throat by a mailed glove) etc. Some loan agreements allow for an increase in the interest rate charged as a penalty for missing a payment, or even for late payment, and this can change what the borrower ends up paying ultimately; there is effectively a new amortization schedule becomes applicable from the date of such a change.
