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I was inspired by geckos which can sever their own tails.

I wonder if a creature which has such an ability, especially with a high regenerative power to grow its body parts, can sustain itself over and over by only eating its own body parts, rather than as distraction like geckos do.

It may not make it full, or allow it to do many activities, but I hope at least it is enough to keep this creature alive.

No.

To regenerate requires more energy than the part itself will supply.

To eat the part you have to break it down chemically and then those chemicals are transported through the body and recombined to make new cells.

All of that requires energy.

You started with a severed limb. It cost you energy to digest it and for your body to "build" a new limb from the digested materials.

To get that energy requires you eat something else (or grow limbs that are smaller and smaller each time). Some of what you eat has to be used to process what you eat.

You'll also expend energy severing the limb, healing the wound, preventing and possibly even fighting infection and just staying alive while the very slow process of limb regrowth happens.

This is why, I suspect, regrowing limbs isn't generally used as a survival adaptation in the evolution of creatures. Animals that lose significant parts of their bodies (in nature, without hospitals and medical care) have a higher risk of infection, disease and death not to mention more vulnerability to attack while lacking a complete set of components. It's a generally survival adaption because, mostly, they're less likely to survive, not more likely.

It depends on how you define the regenerative power.

If the regenerative power is similar to that of Werewolves, Trolls and that kind of magic regeneration then yes, he could. These types of regeneration rarely take into account Newton's laws and will generate matter and energy on the fly. So if the creature eats its own limbs and regenerates them for "free" then he could easily get his daily food intake.

If the creature has to generate them out of the energy he eats he's going to be dead after the first time he lobs off an appendage. Healing wounds and accelerated growth is one of the most energy intensive things your body can do. That single arm would barely regenerate your arm because of all the energy and material lost on just homeostasis of your body and the digestion and transport throughout your body.

The short answer is: Yes with magic, no without magic.

Wouldn't you rather have a magical bowl that is always full with fresh nutritious food, perfectly matched to the species that approaches it?

A lot less disgusting and utterly painful for that poor creature. And the magic is the same, or perhaps less.

You need a lot of energy or magic or power to regenerate a body part, and that's in part because it isn't just meat, it's a functional part of the body with nerves and blood vessels and more.

Creating basic food shouldn't be nearly as hard. But it still requires magic or some sort of power source (which can be the sun) to create the food or at least magic or work to harvest and prepare the food to put in the bowl.

It's the same idea. Without magic, you don't get something for free (even with magic there are often limits; it depends on how you set up your magical system).

When geckos sever their tails (for quick getaways from danger) they have to spend a lot of energy to grow them back. Even if they return and eat them, they're not getting anywhere near the calories it takes to regenerate.

Remember, it takes calories to digest food. It's like taking out a loan to pay back previous loans. There's interest on the money you owe and you simply can not sustain the process.

Nor do all the calories you need for regeneration go to edible flesh. There's just too much else you need there. Only a fraction of the energy it takes to grow a body part becomes stored calories in the body part itself.