Is God 1 x 1 x 1 ?

Is God 1/3 + 1/3 + 1/3 = 1?

No, that is the heresy of partism like a megatron connect his 3 parts to make a whole. Each Person in the Godhead are not valued at only 1/3 each.

1 + 1 + 1 = 1

That's is mathematically incoherent.

1 + 1 + 1 = 3

That is tritheism or polytheism.

1 (Father person) x 1 (Son person) x 1 (Holy Spirit person) = 1 (person)

This is modalism which doesn't work as now we have 4 persons.

1 x 1 x 1= 1

If (1 x 1) is the Father and the Son multiplied together, then 1 * (1 x 1) is... the Spirit is one set of the (Father x Son) which makes no sense. The Spirit is not a factor of multiplying the Father an the Son.

A x B x C = ABC

This has the same problem as 1 x 1 x 1. A is not a multiplication of the Father and the Son. Each Person should be distinct.

Sun -> Light -> Heat

This is Arianism since light was created by the Sun.

Water is liquid, solid, gas

This is modalism.

A father, husband, son.

This is modalism.

Humans have a spirit, soul and body.

This most closely resembles what we are after (Heb. 4.12, 1 Thess. 5.23). Each seems to have their own will as the spirit wars against the flesh of the soulical body, and the flesh wars against the spirit. The soul should be a steward, the spirit a mistress and the body a servant, but your free will is strictly in your soul only even though your body gives you world-consciousness, soul self-consciousness and spirit God-consciousness.

Length (1) x Width (1) x Height (1) = 1 cubed

That's a good analogy but there is no personableness in each length.