Squares of 3...34

Theorem

The following pattern holds:

$\ds 4^2$

$=$

$\ds 16$

$\ds 34^2$

$=$

$\ds 1156$

$\ds 334^2$

$=$

$\ds 111 \, 556$

$\ds 3334^2$

$=$

$\ds 11 \, 115 \, 556$

$\ds 33334^2$

$=$

$\ds 1 \, 111 \, 155\, 556$

and so on.

Proof

This theorem requires a proof.
In particular: Simple but tedious.
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Sources

1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): $3334$
1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $3334$