Computer Science (CS) education is being increasingly included in primary school curricula across New Zealand. As a group, Pasifika students are less likely to engage with CS at tertiary level and in the workforce, so understanding more about their engagement with school level CS seems important. A multiple case-study design was used to explore the nature of engagement with CS for six Year 7 and 8 Pasifika students. Data were collected via a drawing task, semi-structured interviews and observations of CS teaching sessions then analysed using inductive thematic analysis. Four themes emerged as important to participant engagement with CS: participation, reification, imagination and alignment. Additionally, several potential barriers and enablers were identified across three broad themes: access, perceptions and affect. Results highlight Pasifika students' need for adequate access to CS education and intentional teaching around its purpose and relevance to their current and future identities.