Earlier there was restriction on the source of funds for claiming deduction u/s 80C of the Income Tax Act, prior to its omission by Finance Act 1990. It was clearly then stated that the payments shall be out of the Income chargeable to tax and there were controversial case laws whether such investments could be made out of borrowed funds or even accumulated incomes. Later the requirement that the payments shall be out of the income chargeable to tax was dropped. Now the only requirement is that the total deductions under Chapter VIA shall not exceed the Gross total income and in respect of deductions relating to incomes, such incomes should be part of gross total income.
In my view, there is no restriction to borrow and pay for the specified expenses / investments u/s 80C, subject to other limitations as applicable.
Edit :
In the case of deduction u/s 80E, however, it is clearly specified that deduction shall be allowed for any amount paid "out of his income chargeable to tax". Hence, the restriction on payments out of borrowed funds is clearly specified here. As a result, the payment of interest on education loan shall be out of "total income chargeable to tax during the previous year". Hence, you cannot borrow and pay the interest on education loan. However, you can borrow for the purpose of repayment of principal amount. Further, you cannot even pay the interest amount out of your accumulated income, i.e., income that is not part of current year income.