You can't precalculate 1111, however, you can precalculate messages that are multiple of 512. The reason is simple, SHA-256 uses 512-bit message block per compression, i.e. the compression function of SHA256 uses 512-bit message inputs and 256-bit previous hash values.
$$C:\{0,1\}^{256}\times \{0,1\}^{512} \to \{0,1\}^{256}$$
and
$$H_i= C(H_{i-1},m_i)$$ where each $m_i$ has 512-bit lenght and $H_0$ is the IV.
To be honest, my input is 32-Byte ones || 32-Byte X || 32-Byte Y, what exactly do I have to precalculate?
32-Byte makes 256 bit, therefore you can pre-calculate only 32-Byte ones || 32-Byte X part.