As pointed out in the question,

the cake is shown at the end of the game.

During the final battle with GLaDOS,

a recipe for cake is given by one of the personality cores you destroy. According to the Portal Unofficial Wiki, the recipe contains "inedible or undesirable ingredients".

Finally according to the answer to this Arqade question:

When GLaDOS is defeated, she says the line "There really was a cake".

All this implies that the cake does actually exist. However it remains unclear whether GLaDOS ever really intended to reward Chell with cake for completing the trials.

As pointed out in the question,

the cake is shown at the end of the game.

During the final battle with GLaDOS,

a recipe for cake is given by one of the personality cores you destroy. According to the Portal Unofficial Wiki, the recipe contains "inedible or undesirable ingredients".

Finally according to the answer to this Arqade question:

When GLaDOS is defeated, she says the line "There really was a cake".

All this implies that the cake does actually exist. However it remains unclear whether GLaDOS ever really intended to reward Chell with cake for completing the trials.

As pointed out in the question,

the cake is shown at the end of the game.

Also during the final battle with GLaDOS,

a recipe for cake is given by one of the personality cores you destroy. According to the Portal Unofficial Wiki, the recipe contains "inedible or undesirable ingredients".

This implies that the cake does actually exist. However it remains unclear whether GLaDOS ever intended to reward Chell with the cake.

As pointed out in the question,

the cake is shown at the end of the game.

During the final battle with GLaDOS,

a recipe for cake is given by one of the personality cores you destroy. According to the Portal Unofficial Wiki, the recipe contains "inedible or undesirable ingredients".

Finally according to the answer to this Arqade question:

When GLaDOS is defeated, she says the line "There really was a cake".

All this implies that the cake does actually exist. However it remains unclear whether GLaDOS ever really intended to reward Chell with cake for completing the trials.