[Pseudoscience-is-malarkey (OP)]

Just to clarify, but I don't mean a small miniature house for pastry or fireplace decoration, I'm talking about one normal sized humans could live in.

[Bored chemist]

Am I allowed to cheat and use another carbohydrate- cellulose?

[alancalverd]

I used to work for a baker who converted flour and sugar into a very nice house through the Trade Process.

[Kryptid]

As a person who bakes cakes regularly (as a hobby: there's no way I'd do this professionally unless I was desperate for money), I can say that would be extremely difficult unless you either have a loose definition of the words "cake" or "house" or you allow for non-conventional circumstances. Cake is, of course, soft and highly compressible. One way I could think of to deal with that would be to build your cake house in the Arctic so that the cold would freeze it. I'd probably go for something dense like a flourless chocolate cake. Make the whole thing into a pyramidal shape, let it freeze, then carve out the inside. Alternatively, make frozen bricks of flourless cake and build an igloo out of them.

[Bored chemist]

Has anyone measured the compressive strength of a sugar cube?

[axscientist]

I believe that it is certainly possible, but it would be gone as soon as it rained. Animals would eat it. It wouldn't be very durable.

[Kryptid]

Has anyone measured the compressive strength of a sugar cube?

Funnily enough, it appears so: https://www.sciencedirect.com/science/article/pii/S0038080616300919#:~:text=Properties%20of%20sugar%20cubes.&text=Unconfined%20compression%20strength%20tests%20(Fig,the%20range%200.7%E2%80%931.3%25.

Unconfined compression strength tests (Fig. 1) indicated a mean strength of 2325 kPa and a standard deviation of 305 kPa.

Concrete has a compressive strength from 17,000 kPa to over 70,000 kPa: https://centralconcrete.com/wp-content/themes/centralconcrete/images/cip/35pr.pdf

[Petrochemicals]

Has anyone measured the compressive strength of a sugar cube?

Funnily enough, it appears so: https://www.sciencedirect.com/science/article/pii/S0038080616300919#:~:text=Properties%20of%20sugar%20cubes.&text=Unconfined%20compression%20strength%20tests%20(Fig,the%20range%200.7%E2%80%931.3%25.

Unconfined compression strength tests (Fig. 1) indicated a mean strength of 2325 kPa and a standard deviation of 305 kPa.

Concrete has a compressive strength from 17,000 kPa to over 70,000 kPa: https://centralconcrete.com/wp-content/themes/centralconcrete/images/cip/35pr.pdf

I would say

Has anyone measured the compressive strength of a sugar cube?

Funnily enough, it appears so: https://www.sciencedirect.com/science/article/pii/S0038080616300919#:~:text=Properties%20of%20sugar%20cubes.&text=Unconfined%20compression%20strength%20tests%20(Fig,the%20range%200.7%E2%80%931.3%25.

Unconfined compression strength tests (Fig. 1) indicated a mean strength of 2325 kPa and a standard deviation of 305 kPa.

Concrete has a compressive strength from 17,000 kPa to over 70,000 kPa: https://centralconcrete.com/wp-content/themes/centralconcrete/images/cip/35pr.pdf

I wouldn't think that sugar lumps are  possible in a house as the tenancy of sugar to attract moisture, it would quickly dissolve. Plus the fart that the compressive strength is far harder to achieve for higher values.

[Bored chemist]

Plus the fart that the compressive strength is far harder to achieve for higher values.

Thanks for those words of wisdom. I am sure we will all treasure them.