Fire Storm

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Can you place the cubes diagonal to each other so that just the corners are touching?

Or do the faces have to be overlapping?

Given the way Cube AoEs are defined, I think you probably do need to have some overlap of the faces. But keep in mind that there's nothing saying the entire face needs to touch.

Sorcerers can cast this.  Be a Storm Sorcerer or Draconic Bloodline (blue or bronze dragon ancestry) and take Transmuted Spell.  Multiclass into Tempest Domain Cleric for 2 levels.  Transmute this spell to deal lightning or thunder damage and use Destructive Wrath with this spell.  Multiclassing into Cleric also grants you heavy armor, 3 extra cantrips, and the bless spell.  

Assuming the answer is that corners don't count as contiguous:

RAW the entirety of the area doesn't have to be contiguous, just for each cube there must be at least one other cube touching it. 5 disjoint groups of 2 cubes each touching is perfectly legal, so in that sense you could do corner-corner as long as each of those cubes has a face overlapping another cube.

Raw all must be touching with their sides. you cant have 5 groups of 2.

Quote from Tsavizard >>

Raw all must be touching with their sides. you cant have 5 groups of 2.

No, five groups of two is totally fine as written. Nothing in the spell description says all the cubes have to be touching; it just says that each cube must be touching at least one other cube. Separate groups of cubes satisfies that requirement as long as each set of cubes has at least two cubes.