Coined after corkage ¹, the noun cakeage denotes, in a restaurant:
– the cutting and serving of a cake that has been brought in by a customer from off the premises;
– hence also a charge levied for this service.

The noun cakeage is also used as a modifier, as in cakeage charge, cakeage fee, etc.

¹ The noun corkage denotes the uncorking of bottles, hence also a charge levied in a restaurant for uncorking and serving every bottle of wine or other liquor that has been brought in by a customer from off the premises.

These are, in chronological order, the earliest occurrences of the noun cakeage that I have found:

1-: From Column 8, published in The Sydney Morning Herald (Sydney, New South Wales, Australia) of Saturday 3^rd August 1985:

A Fairlight reader went with a group of 12 to a northside restaurant for a birthday dinner a few days ago. One of the party brought a birthday cake. The restaurant put candles on it, cut it up and served it. The group was astounded when the bill included a charge for “Cakeage—$36.”

2-: From Now for Cafe Maxim’s, by Claude Forell, published in The Age (Melbourne, Victoria, Australia) of Tuesday 17^th February 1987:

Corkage we know and resent. But cakeage? Yes, an angry young reader rang to complain that a snazzy South Yarra brasserie had added $1 a head to the bill of nearly $200 for a party of 12 for cutting and serving (after, not instead of, dessert) a surprise birthday cake he and his friends had brought for his fiancee.
A resulting dispute over the surcharge cast a cloud of [sic] what was meant to be a happy celebration. No doubt the restaurant’s management was within its rights, but was its apparent meanness and arrogance sensible? Twelve people won’t be back there, and they will spread the bad word to others.

3-: From Herb Caen’s San Francisco column, published in The Honolulu Advertiser (Honolulu, Hawaii, USA) of Saturday 14^th September 1991:

We all know that if you bring your own bottle of wine to a restaurant, you get charged a corkage fee—but! If you bring your own birthday cake, you could be charged a cakeage fee. At Green’s for instance, it’s $1.50 a person, which annoyed the hell out of Millie Howie. ²

² Mildred Howie (née Carter – 1922-2011) was a U.S. wine writer.

4-: From The Press Democrat (Santa Rosa, California, USA) of Wednesday 27^th May 1992:

Corkage, cakeage fees?

Corkage fee, maybe you’ve heard of.
If you bring your own bottle of wine to a restaurant, they’ll charge you a corkage fee—between $5 and $10 locally—to open it.
But have you ever heard of a CAKEage fee?
People are increasingly celebrating special events in restaurants and they often want to bring their own cake.
As a result, many restaurants are beginning to charge a fee. The going rate is between $1 and $2.50 a plate.
“People have to realize,” chef Lisa Hemenway says “that every day is somebody’s birthday.”

5-: From Have your cake and pay, too: Restaurant adds charge, by Marlaina Gayle, published in The Province (Vancouver, British Columbia, Canada) of Tuesday 21^st July 1992:

You’ve heard of “corkage?”
Well, now there’s “cakeage.”
Corkage is when you take your own bottle of wine to a restaurant, which charges a fee for decanting and serving. This is done around the world.
Now a Robson Street restaurant, Cincin, is charging patrons who bring their own birthday cakes for dessert.
Says owner Jack Evrensel: “We charge $1.50 per person for bringing their own cake. It’s a service we provide. We put it on our plates and use our cutlery. We don’t want cake served on a paper plate or passed around on a napkin.”
Customers are informed of the charge before they bring a cake, he says.
The restaurant charges $4.95 a glass for corkage fee when customers bring their own bottles of special wine.
The cakeage fee has surprised patrons.

In Australian English, corkage and cakeage gave rise to screwage—as Susan Butler, editor of the Macquarie Dictionary, explained to Maria Zijlstra during an ABC (Australian Broadcasting Corporation) radio programme, broadcast on Saturday 29^th January 2011, about the Australian Macquarie Dictionary Word of the Year competition:

Maria Zijlstra: I have a particular favourite, I don’t know whether you do, I don’t know whether you feel free enough to say even if you do, but just before you tell a favourite, if you have one, ‘screwage’ is another good one with a double meaning. I think the literal one is that it’s the charge that you perhaps have to pay at a restaurant. It’s a variation of course on ‘corkage’ but with bottles now having screw tops instead of corks. But it has the added negative connotation of the feeling that you’re perhaps being screwed with this screwage because anyone can of course just unscrew the cap.
Susan Butler: That’s right, someone had to have the bottle opener and take the cork out of the bottle before, but it really has nothing to do with that, it’s just an extra charge from the restaurant, but ‘screwage’ is very humorous and does this job beautifully of conveying that complicated set of attitudes. It’s in a set. First there was ‘corkage’, then there was ‘cakeage’. If you brought your own birthday cake to a restaurant, for instance, you were charged cakeage. And so now we have ‘screwage’ in the set.