Ingress is supposed to be a social game, so yes, destroying an L7 portal on your own is supposed to be hard. Get a friend or two with you and it becomes less hard.
Also to people saying it takes multiple power cubes to destroy a portal, perhaps you aren't approaching it right. You used to be able to stand in the middle and fire off a burst of high level xmps, but now perhaps you want a different strategy: use lower level xmps to save your XM, and fire them from outside the resonator ring to minimise damage. Watch for when the shields break and only then move in for the kill.
Unless you're a smurf, in which case please stand right in the middle and use the highest level xmps you can.